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This paper presents a new iterative algorithm for approximating the invariant points of Suzuki’s generalized nonexpansive maps. Some strong convergence theorems are developed in the context of CAT(0) space. We also included examples to demonstrate the proposed algorithm’s convergence nature. Lastly, the stability of the said iterative algorithm is discussed to validate the results

In this work, the direct and inverse kinematic analysis of both robot arms are investigated based on the analytical and informational representation. The results of the study will be used to provide the functionality of gesturing by a robot in sign language, both Kazakh and other languages, used in educational systems, especially in children's institutions and societies for deaf people. A simulation model of the movement of the robot's arms in the workspace has been studied and built. The developed model will be further implemented and used as mathematical and information support for the created robot. The developed library contains implementations of forward kinematics and iterative algorithms for inverse kinematics. The InMoov robot is a platform widely used in research tasks, supported by the MyRobotLab package. A direct kinematic model for the left and right hands of the robot has been studied. Based on the Python programming language, the working space for robot manipulators was calculated, using the matpilotlib library, an iteration method algorithm was developed to find the probable path of robot manipulators in space. A model of a structured artificial neural network (ANN) is proposed, which is used to find a solution to the inverse kinematics of the InMoov robot with six degrees of freedom (4-dof). The applied ANN model is a multilayer perceptron neural network (MLPNN) in which the learning rule of the Adam-a gradient diskend type is applied. To solve this problem, the problem of finding the best ANN configuration was studied. It has been established that a multilayer parseptron neural network gives the minimum mean square error. The regression coefficient analysis, which shows a 95.6 % fit of all communication variables, is acceptable for obtaining the inverse kinematics of the InMoov robot., У цій роботі досліджується прямий та інверсний кінематичний аналіз обох маніпуляторів на основі аналітичного та інформаційного уявлення. Результати дослідження будуть використані для забезпечення функціоналу жестикуляції роботом мовою жестів як казахською, так і іншими мовами, що використовуються в освітніх системах, особливо в дитячих установах і суспільствах глухих. Досліджено та побудовано імітаційну модель руху рук робота в робочому просторі. Розроблена модель буде надалі реалізована та використана як математичне та інформаційне забезпечення створюваного робота. Розроблена бібліотека містить реалізації алгоритмів прямої кінематики та ітераційних алгоритмів зворотної кінематики. Робот InMoov — платформа, що широко використовується в дослідницьких завданнях, підтримувана пакетом MyRobotLab. Досліджено пряму кінематичну модель для лівої та правої руки робота. На основі мови програмування Python розрахований робочий простір для роботів-маніпуляторів, з використанням бібліотеки matpilotlib розроблено алгоритм методу ітерацій для знаходження ймовірного шляху руху роботів-маніпуляторів у просторі. Запропоновано модель структурованої штучної нейронної мережі (ШНМ), яка використовується для вирішення зворотної кінематики робота InMoov із шістьма ступенями свободи (4-ступеня свободи). Модель ШНМ, що застосовується, являє собою багатошарову персептронну нейронну мережу, в якій застосовується правило навчання типу Адама-градієнтного диска. Для вирішення цієї проблеми було вивчено завдання пошуку найкращої конфігурації ШНМ. Встановлено, що мінімальну середньоквадратичну помилку дає багатошарова нейронна мережа парсептрон. Аналіз коефіцієнтів регресії, який показує збіг всіх комунікаційних змінних на 95,6 %, прийнятний для отримання інверсної кінематики робота InMoov.

Understanding complicated city traffic patterns has been recognized as a critical goal by twenty-first-century urban planners and traffic management systems, resulting in a significant rise in the quantity and variety of traffic data gathered. For example, in a growing number of large cities, taxi firms have begun collecting metadata for each vehicle trip, such as origin, destination, and travel duration. Taxi data offer information on traffic patterns, allowing the study of urban flow—what will traffic look like between two sites on a particular day and time in the future? This paper proposes a method based on sparse GPS probe data, that focuses on allocating travel time data to the different links traveled between GPS observations. This model incorporates the progressive spatial correlations between the links in a network. The main goal of this work is to show how we can consider progressive spatial correlations and improve our results more realistically with a simple adjustment in the previously known parametric methods. For estimating arterial travel time, the methodology is applied to a case study for the partial network of New York City-based on the data collected from the taxicabs in New York City, providing the locations of origins, destinations, and travel times. The model estimates quarter-hourly averages of urban link travel times using OD trip data. This study proposes a more accurate approach for estimating link travel times, that fully utilizes the partial information received from taxi data in cities., IEEE Open Journal of Intelligent Transportation Systems, 3, ISSN:2687-7813

International audience; Image reconstruction from a sequence of a few linear measurements that are corrupted by signal-dependent normally distributed noise is an inverse problem with many biomedical imaging applications, such as computerized tomography and optical microscopy. In this study, we focus on single-pixel imaging, where the set-up acquires a down-sampled Hadamard transform of an image of the scene. Deep learning is a computationally efficient framework to solve inverse problems in imaging. Several neural-network architectures provide a link between deep and optimization-based image reconstruction methods. These deep-learning methods rely on a forward operator and lead to more interpretable networks. Here, we propose a novel network architecture obtained by unrolling an heuristic expectation-maximization algorithm. In particular, we compute the maximum a posteriori estimate of the unknown image given measurements corrupted by normally distributed signal-dependent noise. We show that the so-called expectation-maximization reconstruction network (EM-Net) applies to mixed Skellam-Gaussian noise models that are common in single-pixel imaging. We present reconstruction results from simulated and experimental single-pixel acquisitions. We show that EM-Net generalizes very well to noise levels not seen during training, despite having fewer learned parameters than alternative methods. The proposed EM-Net generally reconstructs images with fewer artifacts and higher signal-to-noise ratios, in particular in high-noise situations compared to other state of the art reconstruction algorithms that do not estimate the noise covariance.

In this work we derive a generalized series expansion of the acrtangent function by using the enhanced midpoint integration (EMI). Algorithmic implementation of the generalized series expansion utilizes two-step iteration without surd and complex numbers. The computational test we performed reveals that such a generalization improves accuracy in computation of the arctangent function by many orders of the magnitude with increasing integer $M$, associated with subintervals in the EMI formula. The generalized series expansion may be promising for practical applications. It may be particularly useful in practical tasks, where extensive computations with arbitrary precision floating points are needed. The algorithmic implementation of the generalized series expansion of the arctangent function shows a rapid convergence rate in the computation of digits of $\pi$ in the Machin-like formulas., Comment: 17 pages, 3 figures

Introduction. Spectrally efficient frequency division multiplexing (SEFDM) is a promising technology for improving spectral efficiency. Since SEFDM signals transmitted on subcarriers are not orthogonal, interchannel interference occurs due to the mutual influence of signals transmitted on adjacent subcarriers. Algorithms for receiving SEFDM signals can be distinguished into element-by-element coherent detection and maximum-likelihood sequence estimation (MLSE). The former method, although being simpler, is characterized by a low bit error rate performance. The latter method, although providing for a higher energy efficiency, is more complicated and does not allow high absolute message rates.Aim. To consider a trade-off solution to the problem of coherent detection of SEFDM signals under the condition of significant interchannel interference, namely, the use of an iterative algorithm of element-by-element processing with decision feedback at each subcarrier frequency.Materials and methods. Analytical expressions for the operation of a demodulator solver were derived. A simulation model for transmission of SEFDM signals was built in the MatLab environment, including element-by-element detection with decision feedback.Results. The simulation results confirmed the efficiency of the proposed algorithm. For error probabilities p =102…103, the energy gains reach values from 0.2 to 7.5 dB for different values of the non-orthogonal subcarrier spacing. At the same time, the efficiency of the detection algorithm with decision feedback turns out to be significantly lower than that when using the detection algorithm MLSE.Conclusion. The proposed detection algorithm can be used in future generations of mobile communications, which require high transmission rates. By reducing the computational complexity of the algorithm, it is possible to provide for a lower power consumption of mobile devices.

Due to the low efficiency of energy harvest (EH) for the traditional wireless powered communication network (WPCN), we propose a communication scheme based on unmanned aerial vehicle (UAV)-enabled WPCN, which can greatly improve the EH efficiency problem. In this paper, the UAV trajectory, time allocation, transmit power of UAVs, scheduling of wireless information transfer (WIT) and wireless power transfer (WPT) are jointly optimized to minimize the whole energy consumption. To solve the formulated non-convex problem with multiple constraints and attain locally optimal solution, an iterative algorithm is proposed. Simulations show that our proposed algorithm is superior to other benchmark algorithms.

This paper investigates the problem of sliding mode controller design based on output feedback for discrete-time Markov jump systems. Considering the typical asynchronous phenomenon for jump systems, here we adopt the Hidden Markov Model (HMM) to quantify the asynchronous degree. Based on this, a static output feedback sliding surface is constructed. Sufficient conditions in terms of bilinear matrix inequalities are proposed ensuring the sliding motion dynamic to be stochastically stable and its $\mathcal {H}_\infty $ performance for the considered discrete time Markov jump systems. Moreover, the reachability of the sliding mode surface is ensured by a predesigned control law. The whole design scheme is presented by using an iterative algorithm. Finally, simulation results are presented to illustrate the effectiveness of the design methodology.

Fast charging is a promising way for plug-in electric vehicles (PEVs) to get recharged quickly and reduce the impacts of long-lasting charging process on PEV owners’ daily life. Decreasing time during charging PEVs also makes the decision of PEV owners choosing where to charge affected more by the time length of driving towards and waiting in charging stations, raising new requirements for charging facilities planning. In this study, a cost minimisation planning method of PEV fast-charging stations taking influences of queuing and driving time into consideration is proposed and solved by the genetic algorithm-based methodology. An iterative algorithm obtaining the equilibrium of the user's decision of place to charge is proposed to consider the impacts of waiting and driving time at different charging stations on PEV owners. The effectiveness of the proposed strategy is then verified through the case analysis based on trajectory data of taxis in Beijing, which shows that the proposed methodology has good performances in computation. Weight of time costs and investment restrictions such as the number of charging stations would also influence the planning result.

Surface potential-based compact models are an essential link between circuit simulation and technology due to their physical base. Such models are particularly important for the development of devices and circuits based on new wide-bandgap semiconductors such as silicon carbide (SiC) where additional physical phenomena in comparison to silicon are considered. An efficient computation of the surface potential ( $\Phi _{\text {S}}$ ) is one of the core components of $\Phi _{\text {S}}$ -based compact models. We developed a fast and robust iterative algorithm for the surface potential, which takes the specific interface trap distribution of SiC-MOSFETs into account. Therefore, a new initial guess is derived, which reduces the number of required iteration steps by 40% in contrast to the common initial guess for silicon devices. Furthermore, different starting equations and types of iteration steps are compared in terms of convergence speed and stability over a wide range of densities of interface traps, technology parameters, and operating conditions.

The phase-shifting interferometry has been intensively studied for more than half a century, and is still actively investigated and improved for more demanding precision measurement requirements. A proper phase-shifting algorithm (PSA) for phase extraction should consider various error sources including (i) the phase-shift errors, (ii) the intensity harmonics, (iii) the non-uniform phase-shift distributions and (iv) the random additive intensity noise. Consequently, a large pool of PSAs has been developed, including those with known phase shifts (abbreviated as kPSA) and those with unknown phase shifts (abbreviated as uPSA). While numerous evaluation works have been done for the kPSAs, there are very few for the uPSAs, making the overall picture of the PSAs unclear. Specifically, there is a lack of (i) fringe pattern parameters' restriction analysis for the uPSAs and (ii) performance comparison within the uPSAs and between the uPSAs and the kPSAs. Thus, for the first time, we comprehensively evaluated the pre-requisites and performance of four representative uPSAs, the advanced iterative algorithm, the general iterative algorithm (GIA), the algorithm based on the principal component analysis and the algorithm based on VU factorization, and then compare the uPSAs with twelve benchmarking kPSAs. From this comparison, the demand for proper selection of a kPSA, and the restriction and attractive performance of the uPSAs are clearly depicted. Due to the outstanding performance of the GIA, a hybrid kPSA-GIA is proposed to boost the performance of a kPSA and relieve the fringe density restriction of the GIA. Economic Development Board (EDB) Ministry of Education (MOE) Published version Economic Development Board - Singapore (S17-1579-IPP-II); Ministry of Education - Singapore (MOET2EP20220-0008).

Real-time acquisition and visualization of temperature anomalies in building spaces and 3D temperature field data during fires are of vital importance for fire danger warnings, early rescue operations, evacuation commands, and subsequent fire accident investigations. Taking into account the non-contact, global (planar and spatial), and high efficiency advantages of acoustic CT temperature measurement technology, this study involved the conducting of exploratory preliminary research in order to provide new ideas for the real-time global perception of information on building fires. The detailed research objective was as follows: obtain the temperature data at any time of a fire based on Fire Dynamics Simulator (FDS) and fit them to form the base temperature distribution diagram at that time. The large ill-conditioned matrix equation of acoustic flight under the scheme of multi-grid division was then constructed. The discrete temperature data of each grid in the building space was obtained by solving the matrix equation based on algebraic reconstruction algorithm (ART) and joint algebraic reconstruction algorithm (SART). The three-dimensional temperature field reconstruction of building space was realized by the interpolation of discrete temperature data. The reconstruction effect of each scheme was evaluated through the error analysis between the reconstruction data and the basic data. The results show that the real-time reconstruction of a 3D temperature field of a building thermal field can be realized based on acoustic CT temperature measurement technology, and the reconstruction algorithm and grid division scheme have a significant control effect on the reconstruction effect.

A new optimization approach is considered in the class of polynomial in-state optimal control problems with constraints based on nonlocal control improvement conditions, which are constructed in the form of special fixed-point problems in the control space. The proposed method of successive approximations of control retains all constraints at each iteration and does not use the operation of parametric variation of control at each iteration, in contrast to known gradient methods. In addition, the initial approximation of the iterative process may not satisfy the constraints, which is a significant factor in increasing the efficiency of the approach. The comparative efficiency of the proposed method of fixed points in the considered class of problems is illustrated in a model example.

A new generalized Yosida inclusion problem, involving A-relaxed co-accretive mapping, is introduced. The resolvent and associated generalized Yosida approximation operator is construed and a few of its characteristics are discussed. The existence result is quantified in q-uniformly smooth Banach spaces. A four-step iterative scheme is proposed and its convergence analysis is discussed. Our theoretical assertions are illustrated by a numerical example. In addition, we confirm that the developed method is almost stable for contractions. Further, an equivalent generalized resolvent equation problem is established. Finally, by utilizing the Yosida inclusion problem, we investigate a resolvent equation problem and by employing our proposed method, a Volterra–Fredholm integral equation is examined.

Poisson surface reconstruction (PSR) remains a popular technique for reconstructing watertight surfaces from 3D point samples thanks to its efficiency, simplicity, and robustness. Yet, the existing PSR method and subsequent variants work only for oriented points. This paper intends to validate that an improved PSR, called iPSR, can completely eliminate the requirement of point normals and proceed in an iterative manner. In each iteration, iPSR takes as input point samples with normals directly computed from the surface obtained in the preceding iteration, and then generates a new surface with better quality. Extensive quantitative evaluation confirms that the new iPSR algorithm converges in 5-30 iterations even with randomly initialized normals. If initialized with a simple visibility based heuristic, iPSR can further reduce the number of iterations. We conduct comprehensive comparisons with PSR and other powerful implicit-function based methods. Finally, we confirm iPSR's effectiveness and scalability on the AIM@SHAPE dataset and challenging (indoor and outdoor) scenes. Code and data for this paper are at https://github.com/houfei0801/ipsr. Ministry of Education (MOE) This research has been partially supported by National Natural Science Foundation of China (61872347, 62072446), Special Plan for the Development of Distinguished Young Scientists of ISCAS (Y8RC535018), National Science Foundation (IIS-1715985 & 1812606 to Qin), Singapore Ministry of Education (MOE-T2EP20220-0005 and RG20/20) and RIE2020 Industry Alignment Fund – Industry Collaboration Projects (IAF-ICP) Funding Initiative, as well as cash and in-kind contribution from the industry partner(s).

In this paper, GNSS interferometric reflectometry (GNSS-IR) is firstly proposed to estimate ground surface subsidence caused by underground coal mining. Ground subsidence on the main direction of a coal seam is described by using the probability integral model (PIM) with unknown parameters. Based on the laws of reflection in geometric optics, model of GNSS signal-to-noise (SNR) observation for the tilt surface, which results from differential subsidence of ground points, is derived. Semi-cycle SNR observations fitting method is used to determine the phase of the SNR series. Phase variation of the SNR series is used to calculate reflector height of ground specular reflection point. Based on the reflector height and ground tilt angle, an iterative algorithm is proposed to determine coefficients of PIM, and thus subsidence of the ground reflection point. By using the low-cost navigational GNSS receiver and antenna, an experimental campaign was conducted to validate the proposed method. The results show that, when the maximum subsidence is 3076 mm, the maximum relative error of the proposed method-based subsidence estimation is 5.5%. This study also suggests that, based on the proposed method, the navigational GNSS instrument can be treated as a new type of sensor for continuously measuring ground subsidence deformation in a cost-effective way.

Sampling and reconstruction of signals in a shift-invariant space are generally studied under the requirement that the generator is in a stronger Wiener amalgam space, and the error estimates are usually given in the sense of $L_{p,{1 / \omega }}$ L p , 1 / ω -norm. Since we often need to reflect the local characteristics of reconstructing error, the asymptotic pointwise error estimates for nonuniform and average sampling in a non-decaying shift-invariant space are discussed under the assumption that the generator is in a hybrid-norm space. Based on Lemma 2.1–Lemma 2.6, we first rewrite the iterative reconstruction algorithms for two kinds of average sampling functionals and prove their convergence. Then, the asymptotic pointwise error estimates are presented for two algorithms under the case that the average samples are corrupted by noise.

Digital predistortion (DPD) is known as an efficient solution to suppress nonlinear distortion of power amplifiers (PAs) in wireless transmitters to achieve both high linearity and power efficiency. In multiple input and multiple output (MIMO) applications, the power gains of multiple transmitting channels are usually different. Meanwhile, the channel crosstalk cannot be ignored, given the isolations between the physical channels are limited. Accordingly, the linearization performances of the conventional DPD methods are usually degraded. In this article, we propose a novel DPD method for MIMO transmitters, where both the crosstalk and different power gains of multiple channels are considered. In this method, the expected predistorted signals, which would be used to train the DPD model, are firstly obtained by an iterative algorithm derived from the contraction mapping theorem. Then, the coefficients of a MIMO-DPD model are extracted by fitting the DPD model to the obtained predistorted signal. Experimental results verify that the extracted coefficients can achieve an improved linearization performance for the MIMO transmitter with crosstalk between the channels, especially in the case where the channel gains are different. Specifically, for a $2 \times 2$ MIMO transmitter with −20 dB crosstalk and 1.2 dB difference between the two channel gains, the proposed DPD improves the adjacent channel power ratio (ACPR) from −31.4 dBc to −47.1 dBc, which outperforms the conventional DPD by 6.8 dB.

This paper studies a full-duplex symbiotic radio network, where a full-duplex access point (FAP) transmits downlink orthogonal frequency division multiplexing signals to a legacy user (LU) and simultaneously receives signals backscattered from multiple passive backscatter devices (BDs) with capability of radio-frequency energy harvesting. A non-orthogonal-multiple-access enhanced dynamic-time-division-multiple-access (NOMA-DTDMA) transmission scheme is proposed to exploit the channel dynamics and further improve the spectrum efficiency. In order to maximize the throughput performance and ensure BD fairness, we maximize the minimum throughput among all BDs by jointly optimizing the FAP's subcarrier power allocation, the BDs' backscatter time allocation and power reflection coefficients, subject to the LU's throughput requirement, the BDs' harvested energy requirements, and other practical constraints. An efficient iterative algorithm is proposed to solve the formulated non-convex problem, by utilizing the block coordinated descent and successive convex optimization techniques. The convergence and complexity of the proposed algorithm are also analyzed. Numerical results show that the proposed NOMA-DTDMA scheme significantly outperforms the benchmark scheme of dynamic TDMA in terms of both throughput performance and BD fairness. Also, the trade-off performances between the BDs' throughput and the LU's throughput requirement as well as the BDs' harvested energy requirements are numerically verified.

With the advent of advanced energy management systems in distribution systems, there is a growing interest in rapid and reliable code for distribution system state estimation (DSSE) in large-scale systems. Fast DSSE methods employed in the industry are based on load scaling as they are well suited to the abundance of pseudo-measurements. Due to the paucity of real-time measurements in DSSE, phasor measurement units (PMUs) have been proposed as a potential solution to increase the estimation accuracy. However, load scaling methodologies are not extendable for exploiting PMUs. This paper proposes a high-performance DSSE method that can handle the PMUs together with all common measurement types in industrial DSSE. By using Wirtinger calculus, the method operates entirely in complex variables and employs the latest version of advanced vector extensions (AVX-2) to reap the maximum potential of computer processing units. The paper highlights the derivation of complex DSSE in matrix form, from which one can infer the implications on code reliability and maintenance. Numerical results are reported on large-scale multi-phase distribution systems, and they are contrasted with a publicly available code for DSSE in real variables. The simulation results show that loop unrolling in AVX-2 contributes about a two-fold increase in the solving speed.

Knowledge of the performance of microbial electrolysis cells under a wide range of operating conditions is crucial to achieve high production efficiencies. Characterizing this performance in an experiment, however, is challenging due to either the long measurement times of steady-state procedures or the transient errors of dynamic procedures. Moreover, wide parallelization of the measurements is not feasible due to the high measurement equipment cost per channel. Hence, to speedup this characterization and to facilitate low-cost, yet widely parallel measurements, this paper presents a novel rapid polarization curve measurement procedure with a dynamic measurement resolution that runs on a custom six-channel potentiostat with a current-driven topology. As case study, the procedure is used to rapidly assess the impact of altering pH values on a microbial electrolysis cell that produces H2. A $\times 2$ – $\times 12$ speedup could be obtained in comparison with the state-of-the-art, depending on the characterization resolution (16–128 levels). On top of this speedup, measurements can be parallelized up to $6\times $ on the presented, affordable—42$-per-channel—potentiostat.

This article designs waveform in fast-time domain to optimise high-frequency radar performances embedded in the co-channel interference and coloured noise. Considering the whitening filter is applied for fast-time processing, a novel objective function accounting for both signal to interference plus noise ratio (SINR) and integrated range sidelobe level (IRSL) is introduced and the constant modulus constraint is forced on the probing waveform. An iterative algorithm based on the alternating direction method of multipliers is presented, resolving such non-convex quartic optimisation problem with a polynomial-time computational complexity. In each iteration, two quadratic problems are presented, with the closed-form solutions given. Finally, the authors evaluate the effectiveness of the designed waveform in terms of the range-Doppler processing result, SINR, IRSL and power spectrum.

This article describes a new interactive design approach integrating the constraints associated with production include manufacturing and assembling. The proposed method, in the form of an algorithm, allows optimisation of product design by minimizing production costs at each iteration, without compromising its functionality. The novelty of this algorithm in terms of modeling and optimisation of production costs in the design phase is its ability to dynamically evaluate the cumulative costs of production as a function of design and procedural choices. The availability of this information first allows the identification of design points and/or procedural points that generate significant production costs, and second, suggests improvements and recommendations that aim to optimize production costs. These experiments were conducted at a smart factory installed in our organisation. The proposed algorithm involves four steps. To optimise production costs, the designer must input all of the required data into the simulation and thereby identify the most significant cost elements to optimise. Then, the designer uses the suggested recommendation list to modify the relevant design and/or manufacturing parameters, thus obtaining the new, optimised production costs. If the first result is unsatisfactory, other iterations can be performed.

The point of this research is to present a new iterative procedure for approximating common fixed points of nonexpansive mappings in Hadamard manifolds. The convergence theorem of the proposed method is discussed under certain conditions. For the sake of clarity, we provide some numerical examples to support our results. Furthermore, we apply the suggested approach to solve inclusion problems and convex feasibility problems.

Support estimation (SE) of a sparse signal refers to finding the location indices of the nonzero elements in a sparse representation. Most of the traditional approaches dealing with SE problems are iterative algorithms based on greedy methods or optimization techniques. Indeed, a vast majority of them use sparse signal recovery (SR) techniques to obtain support sets instead of directly mapping the nonzero locations from denser measurements (e.g., compressively sensed measurements). This study proposes a novel approach for learning such a mapping from a training set. To accomplish this objective, the convolutional sparse support estimator networks (CSENs), each with a compact configuration, are designed. The proposed CSEN can be a crucial tool for the following scenarios: 1) real-time and low-cost SE can be applied in any mobile and low-power edge device for anomaly localization, simultaneous face recognition, and so on and 2) CSEN’s output can directly be used as “prior information,” which improves the performance of sparse SR algorithms. The results over the benchmark datasets show that state-of-the-art performance levels can be achieved by the proposed approach with a significantly reduced computational complexity. publishedVersion

In this paper, we suggest and analyze an iterative algorithm to approximate a common solution of a hierarchical fixed point problem for nonexpansive mappings, a system of variational inequalities, and a split equilibrium problem in Hilbert spaces. Under some suitable conditions imposed on the sequences of parameters, we prove that the sequence generated by the proposed iterative method converges strongly to a common element of the solution set of these three kinds of problems. The results obtained here extend and improve the corresponding results of the relevant literature.

In the paper, we determine the period of an n-dimensional nonlinear dynamical system by using a derived formula in an (n + 1)-dimensional augmented space. To form a periodic motion, the periodic conditions in the state space and nonlinear first-order differential equations constitute a special periodic problem within a time interval with an unknown length. Two periodic problems are considered: (a) boundary values are given and (b) boundary values are unknown. By using the shape functions, a boundary shape function method (BSFM) is devised to obtain an initial value problem with the initial values of the new variables given. The unknown terminal values of the new variables and period are determined by two iterative algorithms for the case (a) and one iterative algorithm for the case (b). The periodic solutions obtained from the BSFM satisfy the periodic conditions automatically. For the numerical example, the computed order of convergence displays the merit of the BSFM. For the sake of comparison, the iterative algorithms based on the shooting method for cases (a) and (b) were developed by directly implementing the Poincaré map into the fictitious time-integration method to determine the period. The BSFM is better than the shooting method in terms of convergence speed, accuracy, and stability.

This paper deals with solvability and algorithms for a new class of generalized nonlinear variational-like inequalities in reflexive Banach spaces. By employing the Banach’s fixed point theorem, Schauder’s fixed point theorem, and FanKKM theorem, we obtain a sufficient condition which guarantees the existence of solutions for the generalized nonlinear variational-like inequality. We introduce also an auxiliary variational-like inequality and, by utilizing the minimax inequality, get the existence and uniqueness of solutions for the auxiliary variational-like inequality, which is used to suggest an iterative algorithm for solving the generalized nonlinear variational-like inequality. Under certain conditions, by means of the auxiliary principle technique, we both establish the existence and uniqueness of solutions for the generalized nonlinear variational-like inequality and discuss the convergence of iterative sequences generated by the iterative algorithm. Our results extend, improve, and unify several known results in the literature.

This paper focuses on the stabilization problem for rectangular descriptor fractional order systems (FOSs) with $0

Complementary sets of sequences (CSSs) are widely used in many applications, such as active sensing and wireless communication. The construction of CSS has attracted considerable attention over the past few decades. In this paper, efficient and comprehensive computational algorithms for CSS design are proposed. We seek to minimize complementary integral sidelobe level (CISL) under multiple constraints, including unimodular, peak-to-average power ratio, discrete phase, and spectrum compatible constraint. The task of CSS design can be formulated as solving a nonconvex constraint optimization problem. As this problem is difficult to tackle directly, we resort to the general majorization-minimization (MM) method. By utilizing the inherent algebraic structure of the objective function, we construct the majorizing function via two consecutive applications of the MM method and obtain a closed-form solution by a couple of FFT operations at each iteration. The relationship between MM-based algorithms and derivative-based algorithms is revealed. Our algorithms are more flexible and widely applicable, and the numerical experiment results demonstrate the effectiveness and superiority over the existing state-of-art algorithms.

In this study, considering the advantages of parallel fixed point algorithms arising from their symmetrical behavior, new types of parallel algorithms have been defined. Strong convergence of these algorithms for certain mappings with altering points has been analyzed, and it has been observed that their convergence behavior is better than existing algorithms with non-simple samples. In addition, the concept of data dependency for these algorithms has been examined for the first time in this study. Finally, it has been proven that the solution of a variational inequality system can be obtained using newly defined parallel algorithms under suitable conditions.

The flooding of railway ballasts can cause extensive damage. This process has been the subject of several experimental investigations. In the present work, a relatively easy to implement approach to modelling this fluid flow is presented. It is shown that good agreement with the experimental results is obtained. The fluid flow is modelled by Darcy’s law, which we extend to the free fluid flowing above the ballast. The main complexity is in determining the free surface position, which is accomplished using an iterative procedure. The equations are solved using the finite element method. The method is illustrated by careful numerical calculations that are carefully compared with the experimental results reported in the literature. The method is then extended to realistic railway ballast, including the effects of ballast fouling. It is shown that when the flow begins to overtop the ballast, the free surface shifts to greatly increase the chance of ballast scouring.

In the early 1930s, Erwin Schrodinger, motivated by his quest for a more classical formulation of quantum mechanics, posed a large deviation problem for a cloud of independent Brownian particles. He showed that the solution to the problem could be obtained through a system of two linear equations with nonlinear coupling at the boundary (Schrodinger system). Existence and uniqueness for such a system, which represents a sort of bottleneck for the problem, was first established by Fortet in 1938/1940 under rather general assumptions by proving convergence of an ingenious but complex approximation method. It is the first proof of what are nowadays called Sinkhorn-type algorithms in the much more challenging continuous case. Schrodinger bridges are also an early example of the maximum entropy approach and have been more recently recognized as a regularization of the important optimal mass transport problem. Unfortunately, Fortet’s contribution is by and large ignored in contemporary literature. This is likely due to the complexity of his approach coupled with an idiosyncratic exposition style and due to missing details and steps in the proofs. Nevertheless, Fortet’s approach maintains its importance to this day as it provides the only existing algorithmic proof, in the continuous setting, under rather mild assumptions. It can be adapted, in principle, to other relevant optimal transport problems. It is the purpose of this paper to remedy this situation by rewriting the bulk of his paper with all the missing passages and in a transparent fashion so as to make it fully available to the scientific community. We consider the problem in $${\mathbb {R}}^d$$ rather than in $${\mathbb {R}}$$ and use as much as possible his notation to facilitate comparison.

The order-of-addition generalization simplex-centroid designs play a key role in mixture experiments, for example, the mixture experiments with process variables. The paper formally combines order-of-addition (OofA) with mixture components in the same experiment. This paper proposes a new algorithm which generates full OofA mth-degree generalization simplex-centroid designs for q components by a class of the direction graphs, and a series of examples also confirms the value of the proposed algorithm.

The problem of influence maximization (IM) has been extensively studied in recent years and has many practical applications such as social advertising and viral marketing. Given the network and diffusion model, IM aims to find an influential set of seed nodes so that targeting them as diffusion sources will trigger the maximum cascade of influenced individuals. The largest challenge of the IM problem is its NP-hardness, and most of the existing approaches are with polynomial time complexity, making themselves unscalable to very large networks. To address this issue, in this paper, we propose LAIM: a linear time iterative approach for efficient IM on large-scale networks. Our framework has two steps: 1) influence approximation and 2) seed set selection. In the first step, we propose an iterative algorithm to compute the local influence of a node based on a recursive formula and use the local influence to approximate its global influence. In the second step, the $k$ influential seed nodes are mined based on the approximated influence in the first step. Based on our model, we theoretically prove that the proposed approach has linear time and space complexity. We further accelerate our algorithm with simple modifications and propose its fast version. Experimental results on eight real-world large-scale networks exhibit the superiority of our approach over the state-of-the-art methods in terms of both effectiveness and efficiency.

The problem of state estimation for discrete-time stochastic time-varying systems in the presence of unknown process inputs or disturbances is addressed in this paper. A Kalman-type filter is proposed, and the optimal oracle filter gain in the sense of minimizing the mean squared error of the state estimate is obtained. To tackle the unknown quantities in the gain matrix, a nonlinear equation is introduced and its solution is taken as the estimate of unknown inputs, and then, a novel nonlinear equation-based unknown input filtering (NEUIF) is proposed. A scalar-based iterative algorithm for related fixed point problem is developed so that the dichotomy method is employed to solve the above nonlinear equation very efficiently. Adopting the same strategy for the dynamic systems with unknown inputs or disturbances, we provide two applications of the proposed state estimation algorithm. One is for a class of nonlinear dynamic systems with linear observations by taking the residual term in linearizing the transition function as an unknown input in the derived linear system. The other is for tracking maneuvering targets in which the bias between the real motion and modeled motions is regarded as an unknown input in the state transition equation. Some numerical simulations demonstrate the effectiveness of the proposed NEUIF method for tackling various uncertainties in complicated dynamic systems.

With the rapid development of technologies like the Internet, sensors and bioinformatics, and data has grown explosively. In the big data era, more and more iterative algorithms have been applied in the fields of data mining and machine learning. In most situation, the iterative algorithms compute in the entire dataset which are merged from the partial ones. Given the iterative results on partial datasets, it is efficient if the results on the entire dataset can be merged from them, otherwise the re-computing on entire one is time consuming. Unfortunately, current iteration model do not support the results merging. We propose merge iteration computing model (Mim) in this paper. Mim is a solution but not a platform. It states how to execute iterative algorithm effectively through reusing the exiting results without sacrificing the accuracy, and such mechanism is suitable for the most iterative algorithms. We explain the in-partition iteration step, error evaluation step, compensation step (optional), and merge iteration step of Mim, in addition, the in-partition iteration step is preliminary of merging iteration and should be done before the partial datasets are merged. We also analyze the accuracy and performance advantages of Mim theoretically. In the application scenarios, we implement Mim over Spark framework, and applied the Mim to the financial data analysis in a city. Finally, through a series of experiments, we prove the efficiency and accuracy of the proposed Mim on the PageRank and K-means algorithms. Under the various test cases, the maximum optimization ratio of Mim is 25% and 56% comparing with regular iteration on PageRank and K-means, respectively. And the errors are negligible.

Since traffic origin-destination (OD) demand is a fundamental input parameter of urban road network planning and traffic management, multisource data are adopted to study methods of integrated sensor deployment and traffic demand estimation. A sensor deployment model is built to determine the optimal quantity and locations of sensors based on the principle of maximum link and route flow coverage information. Minimum variance weighted average technology is used to fuse the observed multisource data from the deployed sensors. Then, the bilevel maximum likelihood traffic demand estimation model is presented, where the upper-level model uses the method of maximum likelihood to estimate the traffic demand, and the lower-level model adopts the stochastic user equilibrium (SUE) to derive the route choice proportion. The sequential identification of sensors and iterative algorithms are designed to solve the sensor deployment and maximum likelihood traffic demand estimation models, respectively. Numerical examples demonstrate that the proposed sensor deployment model can be used to determine the optimal scheme of refitting sensors. The values estimated by the multisource data fusion-based traffic demand estimation model are close to the real traffic demands, and the iterative algorithm can achieve an accuracy of 10−3 in 20 s. This research has significantly promoted the effects of applying multisource data to traffic demand estimation problems.

Tomographic image reconstruction for low-dose computed tomography (CT) is increasingly challenging as dose continues to reduce in clinical applications. Pre-log domain methods and post-log domain methods have been proposed individually and each method has its own disadvantage. While having the potential to improve image quality for low-dose data by using an accurate imaging model, pre-log domain methods suffer slow convergence in practice due to the nonlinear transformation from the image to measurements. In contrast, post-log domain methods have fast convergence speed but the resulting image quality is suboptimal for low dose CT data because the log transformation is extremely unreliable for low-count measurements and undefined for negative values. This paper proposes a hybrid method that integrates the pre-log model and post-log model together to overcome the disadvantages of individual pre-log and post-log methods. We divide a set of CT data into high-count and low-count regions. The post-log weighted least squares model is used for measurements in the high-count region and the pre-log shifted Poisson model for measurements in the low-count region. The hybrid likelihood function can be optimized using an existing iterative algorithm. Computer simulations and phantom experiments show that the proposed hybrid method can achieve faster early convergence than the pre-log shifted Poisson likelihood method and better signal-to-noise performance than the post-log weighted least squares method.

International audience; The problem of estimating a spectral representation of exponentially decaying signals from a set of sampled data is of considerable interest in several applications such as in vibration analysis of mechanical systems. In this paper we present a nonparametric and a parametric method for modal parameter identification of vibrating systems when only output data is available. The nonparametric method uses an iterative adaptive algorithm based in the formation of a two dimensional grid mesh, both in frequency and damping domains. We formulate the identification problem as an optimization problem where the signal energy is obtained from each frequency grid point and damping grid point. The modal parameters are then obtained by minimizing the signal energy from all grid points other than the grid point which contains the modal parameters of the system. The parametric approach uses the state space model and properties of the controllability matrix to obtain the state transition matrix which contains all modal information. We discuss and illustrate the benefits of the proposed algorithms using a numerical and two experimental tests and we conclude that the nonparametric approach is very time consuming when a large number of samples is considered and does not outperform the parametric approach.

In this paper, we introduce an iterative algorithm to approximate a common solution of a generalized equilibrium problem and a fixed point problem for an asymptotically nonexpansive mapping in a real Hilbert space. We prove that the sequences generated by the iterative algorithm converge strongly to a common solution of the generalized equilibrium problem and the fixed point problem for an asymptotically nonexpansive mapping. The results presented in this paper extend and generalize many previously known results in this research area. Some applications of main results are also provided.

A variety of strategies are used to construct algorithms for solving equations. However, higher order derivatives are usually assumed to calculate the convergence order. More importantly, bounds on error and uniqueness regions for the solution are also not derived. Therefore, the benefits of these algorithms are limited. We simply use the first derivative to tackle all these issues and study the ball analysis for two sixth order algorithms under the same set of conditions. In addition, we present a calculable ball comparison between these algorithms. In this manner, we enhance the utility of these algorithms. Our idea is very general. That is why it can also be used to extend other algorithms as well in the same way.

In this paper, we introduce an iterative algorithm for finding a common solution of a finite family of the equilibrium problems, quasi-variational inclusion problems and fixed point problem on Hadamard manifolds. Under suitable conditions, some strong convergence theorems are proved. Our results extend some recent results in literature.

The problem of determining the position of the lidar with optimal accuracy is relevant in various fields of application. This is an important task of robotics that is widely used as a model when planning the route of vehicles, flight control systems, navigation systems, machine learning, and managing economic efficiency, a study of land degradation processes, planning and control of agricultural production stages, land inventory to evaluations of the consequences of various environmental impacts. The paper provides a detailed analysis of the proposed parallelization algorithm for solving the problem of determining the current position of the lidar. To optimize the computing process in order to accelerate and have the possibility of obtaining a real-time result, the OpenMP parallel computing technology is used. It is also possible to significantly reduce the computational complexity of the successive variant. A number of numerical experiments on the multi-core architecture of modern computers have been carried out. As a result, it was possible to accelerate the computing process about eight times and achieve an efficiency of 0.97. It is shown that a special difference in time of execution of a sequential and parallel algorithm manages to increase the number of measurements of lidar and iterations, which is relevant in simulating various problems of robotics. The obtained results can be substantially improved by selecting a computing system where the number of cores is more than eight. The main areas of application of the developed method are described, its shortcomings and prospects for further research are provided.

In this article, we suggest the local analysis of a uni-parametric third and fourth order class of iterative algorithms for addressing nonlinear equations in Banach spaces. The proposed local convergence is established using an ω-continuity condition on the first Fréchet derivative. In this way, the utility of the discussed schemes is extended and the application of Taylor expansion in convergence analysis is removed. Furthermore, this study provides radii of convergence balls and the uniqueness of the solution along with the calculable error distances. The dynamical analysis of the discussed family is also presented. Finally, we provide numerical explanations that show the suggested analysis performs well in the situation where the earlier approach cannot be implemented.

In this paper we consider the following problems:(1) Which weakly Picard operators satisfy a retraction- displacement condition? (2) For which weakly Picard operators the fixed point problem is well posed? (3) Which weakly Picard operators have Ostrowski property?Some applications and open problems are also presented.

With anchor positions and measurements of distances between an object and anchors, positioning algorithms calculate the position of an object, e.g. via lateration. Positioning systems require calibration and configuration prior to operation. In the past, approaches employed reference nodes with GPS or other reference location systems to determine anchor positions. In this article, we propose an approach to determine anchor positions without prior knowledge. We evaluate our approach with simulations and real data based on the Decawave DW1000 radio and show that the error is proportional to the mean error of the distance estimation.

In this paper, we establish generalized sampling theorems, generalized stability theorems and new inequalities in the setting of shift-invariant subspaces of Lebesgue and Wiener amalgam spaces with mixed-norms. A convergence theorem of general iteration algorithms for sampling in some shift-invariant subspaces of Lp→(Rd) are also given.

The aim of this paper is to formulate and analyze a cyclic iterative algorithm in real Hilbert spaces which converges strongly to a common solution of fixed point problem and multiple-sets split common fixed point problem involving demicontractive operators without prior knowledge of operator norm. Significance and range of applicability of our algorithm has been shown by solving the problem of multiple-sets split common null point, multiple-sets split feasibility, multiple-sets split variational inequality, multiple-sets split equilibrium and multiple-sets split monotone variational inclusion.