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Algebraic Riccati matrix equations arise naturally in various situations and their role and application in systems, filtering, stochastic process, and control theory, in particular, have been well established in recent years. This study presents iterative algorithms to solve the algebraic Riccati matrix equation (ARME) R (X) = X D X - X C - B X + A = 0 , based on the weight splitting (WS). We demonstrate that the iterative algorithms converge to non-positive and non-negative solutions of the ARME in special situations. To compare the new algorithms with the previously existing algorithm, we present some numerical examples. [ABSTRACT FROM AUTHOR]

The concept of resolvent operator associated with a P-η-accretive mapping is used in constructing of a new iterative algorithm for solving a new system of generalized multi-valued resolvent equations in the framework of Banach spaces. Some definitions along with some new concrete examples are provided. The main result of this paper is to prove the Lipschitz continuity of the resolvent operator associated with a P-η-accretive mapping and to compute an estimate of its Lipschitz constant under some new appropriate conditions imposed on the parameters and mappings involved in it. In part II, the convergence analysis of the sequences generated by our proposed iterative algorithm under some appropriate conditions is studied. The results presented in this paper are new, and improve and generalize many known corresponding results. [ABSTRACT FROM AUTHOR]

Various studies have explored community-shared solar (CSS) initiatives to help lower energy costs and increase the use of renewable energy sources. Various forms of CSS have been developed worldwide, specifically adapted to meet local economic and environmental conditions as well as technological readiness. This study proposes a variant of CSS that incorporates monthly photovoltaic (PV) rental options and load management functions for households in South Korea, a country characterized by limited land availability, high population density, and extremely high land-use costs. This study evaluates the feasibility of the proposed CSS by assessing the economic benefits for all stakeholders involved, including households, the CSS business (or government), and the grid service provider. It utilizes a mathematical programming model for its formulation and employs an iterative algorithm based on Karush–Kuhn–Tucker conditions for solving it. Additionally, a numerical assessment is conducted with 400 customers classified into three different categories of energy usage. The findings indicate that participating households experienced a reduction in electricity costs ranging from 36.8% to 56.7%, depending on the season and specific scenarios. The CSS business also realized significant profits while the grid service provider benefited from reduced fluctuations in power supply, leading to improved efficiency in grid operations and maintenance. [ABSTRACT FROM AUTHOR]

In this paper, we introduce two novel forward-backward splitting algorithms (FBSAs) for nonsmooth convex minimization. We provide a thorough convergence analysis, emphasizing the new algorithms and contrasting them with existing ones. Our findings are validated through a numerical example. The practical utility of these algorithms in real-world applications, including machine learning for tasks such as classification, regression, and image deblurring reveal that these algorithms consistently approach optimal solutions with fewer iterations, highlighting their efficiency in real-world scenarios. [ABSTRACT FROM AUTHOR]

In this paper, we present a new algorithm for solving split common fixed point problem for asymptotically demicontractive mapping in two real Hilbert spaces. Under some mild conditions, we prove that the proposed method converges strongly to a solution of the problem. We give examples to illustrate that the class of asymptotically demicontractive mappings and the class of demicontractive mappings are independent. Moreover, we give numerical experiments to show the efficiency and applicability of our method in comparison with a related method in the literature. The results obtained unify, improve and extend so many related results in the literature in this direction. [ABSTRACT FROM AUTHOR]

In order to solve the problems of high measurement resources needed, high cost, and low recall rate for anycast enumeration, an anycast enumeration method based on forwarding relationship inference was proposed for anycast-based public DNS resolvers. Based on the observation of the endogenous forwarding relationship between open forwarders and public DNS resolvers, a massive number of open forwarders were transformed into vantage points in measuring public DNS resolvers’anycast instances; Then, through multiple iterations of forwarding relationship measurement, indirect resolver aggregation, and forwarder correlation, the forwarding relationship between forwarders and the DNS resolvers’service addresses was inferred, achieving a spiral enumeration of public parser anycast nodes. Using the publicly available data of Google Public DNS as the benchmark dataset, the experimental results show that the proposed method only requires one measurement machine to recall 62.5% of the airport codes of Google Public DNS’s anycast instances. Compared with existing methods, the recall rate of anycast instance airport codes has increased by 22.92% under the condition of reducing the demand for measurement nodes by 3-4 orders of magnitude.

AbstractThe single-index model (SIM) reveals the intricate relationship between the response variable and covariates, allowing for the consideration of potential heterogeneity and nonlinearity in the data, while also offering interpretability and flexibility. This paper concentrates on estimating the parameters and the unknown link function for the quantile SIM with high-dimensional covariates. We introduce a novel iterative algorithm that strikes a balance between estimation accuracy, computational efficiency, and adaptability to diverse datasets. The initial values for iteration and iteration termination conditions are also discussed. The finite sample performance is illustrated through a simulation study, demonstrating the advantages of our method in terms of accuracy and speed. [ABSTRACT FROM AUTHOR]

In urban metro systems, unexpected events often occur to cause discordance in the planned timetable and delay in passenger travel. Therefore, this study focuses on the timetable rescheduling problem by adopting a stop-skipping strategy during the off-peak period. In addition, there are a number of existing optimization models that minimize the total passenger waiting time, which can cause fairness issues for a small group of passengers having longer waiting time at some stations. In this study, a rescheduling model is proposed to consider passenger waiting time fairness and train travel time cost. This model is tested with a randomly designed delay scenario of Nanjing Metro Line 2, which can be efficiently solved by a designed iterative algorithm based on decomposition method. Compared to the standard stop pattern, the result shows that the stop-skipping pattern can better alleviate the impact of sudden delays, while simultaneously ensuring the passenger waiting time fairness. [ABSTRACT FROM AUTHOR]

This paper proposes new iterative algorithms by using the generalized viscosity implicit midpoint rule in Banach space, which is also a symmetric space. Then, this paper obtains strong convergence conclusions. Moreover, the results generalize the related conclusions of some researchers. Finally, this paper provides some examples to verify these conclusions. These conclusions further extend and enrich the relevant theory of symmetric space. [ABSTRACT FROM AUTHOR]

The aim of this paper is to find the approximate series solution of IVPs on nonlinear differential equations (NDEs) and on systems of NDEs via an iterative algorithm that can be easily exhibited through MATLAB code. We propose a modified iterative scheme based on the DGJM method of solving functional equations of the form u = f + N(u), and we observe that the method is far better than those existing in the literature. For the sake of illustration, series solutions to a few physical equations proposed by Klien-Gordon, Allen- Cahn and Benjamin-Bona-Mahony are provided along with the MATLAB code used for computation. Moreover, graphs are used to validate the efficacy of the method. [ABSTRACT FROM AUTHOR]

The optimal control design of the boiler-turbine system is vital to ensure feasibility and high responsiveness over desired load variations. Using the traditional linear control techniques realization of this task is difficult, as the boiler-turbine mechanism has strong nonlinearities. Besides, environmental and economic concerns have replaced existing tracking control ones as the primary concerns of advanced power plants. Thus, this study proposes an optimal economic model predictive controller (EMPC) scheme for this unit on the basis of the input/output feedback linearization (IOFL) method. By employing the IOFL method, this unit is decoupled into a new linearized model that is utilized for developing the suggested optimal IOFL EMPC technique. The proposed control scheme is formulated in an economic quadratic programming form that considers the input-rate and input limits of the unit for optimal economic performance. In addition, an adaptive iterative algorithm is utilized for constraints mapping with guaranteeing a feasible solution in a finite number of steps without violation of original constraints over the entire predictive horizon. The outcomes of the simulation show that the suggested optimal IOFL EMPC scheme offers an improved dynamic and economic output performance over fuzzy hierarchical MPC, fuzzy EMPC, and nonlinear EMPC techniques during various load variations. • An optimal EMPC scheme based on IOFL method is proposed for boiler-turbine unit. • The IOFL EMPC scheme is formulated in an economic QP form including constraints. • An adaptive iterative algorithm ensures feasible solution without limits violation. • The IOFL EMPC scheme enhances dynamic economic performance for boiler-turbine unit. [ABSTRACT FROM AUTHOR]

To enhance solution accuracy and training efficiency in neural network approximation to partial differential equations, partitioned neural networks can be used as a solution surrogate instead of a single large and deep neural network defined on the whole problem domain. In such a partitioned neural network approach, suitable interface conditions or subdomain boundary conditions are combined to obtain a convergent approximate solution. However, there has been no rigorous study on the convergence and parallel computing enhancement on the partitioned neural network approach. In this paper, iterative algorithms are proposed to enhance parallel computation performance in the partitioned neural network approximation. Our iterative algorithms are based on classical additive Schwarz domain decomposition methods. For the proposed iterative algorithms, their convergence is analyzed under an error assumption on the local and coarse neural network solutions. Numerical results are also included to show the performance of the proposed iterative algorithms. [ABSTRACT FROM AUTHOR]

Panel data model with fixed effects is widely used in economic and administrative applications. However, the presence of factors: measurement errors, data variability and outliers may potentially decrease the accuracy of the model prediction. In this paper, we use panel interval-valued data to represent measurement errors and data volatility of observations. Further, we propose a corresponding panel interval-valued data model with fixed effects, in which both the response and explanatory variables are interval-valued data. To reduce the impact of outliers on our model, we propose a robust estimation method based on the iterative weighted least squares technique. Later, Monte Carlo simulation and empirical application demonstrate that our model is a suitable tool for analyzing the behaviour of panel interval-valued data. [ABSTRACT FROM AUTHOR]

The Gaussian mixture model (GMM) is a probabilistic model that represents the behavior of a data set as a linear combination of K Gaussian densities. The most used method to estimate the parameters of a GMM is the maximum likelihood, giving rise to the EM-algorithm. Another alternative is minimizing the Gini index of dissimilarity between the empirical distribution of the observed data and the parametric distribution GMM, deriving in an iterative algorithm called GID-algorithm. In this work, we prove its convergence with the help of the χ 2 divergence. [ABSTRACT FROM AUTHOR]

In this paper, we develop an effective iterative algorithm to solve a generalized Sylvester tensor equation over quaternions which includes several well-studied matrix/tensor equations as special cases. We discuss the convergence of this algorithm within a finite number of iterations, assuming negligible round-off errors for any initial tensor. Moreover, we demonstrate the unique minimal Frobenius norm solution achievable by selecting specific types of initial tensors. Additionally, numerical examples are presented to illustrate the practicality and validity of our proposed algorithm. These examples include demonstrating the algorithm's effectiveness in addressing three-dimensional microscopic heat transport and color video restoration problems. [ABSTRACT FROM AUTHOR]

In the presence of Banach spaces, a novel iterative algorithm is presented in this study using the Chatterjea–Suzuki–C (CSC) condition, and the convergence theorems are established. The efficacy of the proposed algorithm is discussed analytically and numerically. We explain the solution of the Caputo fractional differential problem using our main result and then provide the numerical simulation to validate the results. Moreover, we use MATLAB R (2021a) to compare the obtained numerical results using the new iterative algorithm with some efficient existing algorithms. The work seems to contribute to the current advancement of fixed-point approximation iterative techniques in Banach spaces. [ABSTRACT FROM AUTHOR]

Project development in river basins is beset with lots of challenges occasioned by human activities which spark off climate variability that hinder their effectiveness to planning and management with other extraneous factors in the area. The study aimed at the use of Game theory model to optimize the net benefits on multi-purpose projects development in Anambra-Imo River basin. The objective was to use the iterative algorithm of game decision theory model to optimize the multi-purpose/multi-objective projects development at the river basin. The methodology involves the use of Game decision theory based on data generated from Bill of Engineering Measurement and Evaluation (BEME), descriptive, experimental model size and simulation modeling solution techniques, correlation and regression analysis. The result shows that the optimal strategies for the game theory was N69.02billion. The value of the name was 5.52 calculated from the Simplex Method Linear Programming Techniques of Game theory which falls between the maximin of 5.77 and minimax of 3.36. The correlation between the probabilities for player A and player B shows a strongly positive correlation 0.9612 which is consistent with that calculated from the graphical activities of r = 0.9635. The work recommends that the implementation of the optimal strategies of Game theory will assist in mitigating the effect of climate variability for improved integrated planning and management of the river basin. The adaptation to climate change condition will deliver benefits in order to achieve global potential contribution to multiple sustainable challenges in the river basin. [ABSTRACT FROM AUTHOR]

High-dimensional but incomplete data are common in many settings. With such data, regularized estimation and variable selection techniques developed for complete data fail to produce reliable results due to the missingness. To address this problem, we propose an iterative penalized least squares estimation (IPLSE) method, which customizes existing penalized regression techniques for data with high missing rates and individual-specific missing patterns. The proposed method simultaneously conducts missing value imputation, parameter estimation, and variable selection. Statistical properties are rigorously established, and a simulation demonstrates its competitive performance under various missing patterns, especially when there is missingness concerning important variables. An analysis of China's provincial economic data further supports the merits of the proposed method. [ABSTRACT FROM AUTHOR]

It is generally known that in order to solve the split equality fixed-point problem (SEFPP), it is necessary to compute the norm of bounded and linear operators, which is a challenging task in real life. To address this issue, we studied the SEFPP involving a class of quasi-pseudocontractive mappings in Hilbert spaces and constructed novel algorithms in this regard, and we proved the algorithms' convergences both with and without prior knowledge of the operator norm for bounded and linear mappings. Additionally, we gave applications and numerical examples of our findings. A variety of well-known discoveries revealed in the literature are generalized by the findings presented in this work. [ABSTRACT FROM AUTHOR]

Given the increasingly severe global fires, the accurate detection of small and fragmented cropland fires has been a significant challenge. The use of medium-resolution satellite data can enhance detection accuracy; however, key challenges in this approach include accurately capturing the annual and interannual variations of burning characteristics and identifying outliers within the time series of these changes. In this study, we focus on a typical crop-straw burning area in Henan Province, located on the North China Plain. We develop an automated burned-area detection algorithm based on near-infrared and short-wave infrared data from Landsat 5 imagery. Our method integrates time-series outlier analysis using filtering and automatic iterative algorithms to determine the optimal threshold for detecting burned areas. Our results demonstrate the effectiveness of using preceding time-series and seasonal time-series analysis to differentiate fire-related changes from seasonal and non-seasonal influences on vegetation. Optimal threshold validation results reveal that the automatic threshold method is efficient and feasible with an overall accuracy exceeding 93%. The resulting burned-area map achieves a total accuracy of 93.25%, far surpassing the 76.5% detection accuracy of the MCD64A1 fire product, thereby highlighting the efficacy of our algorithm. In conclusion, our algorithm is suitable for detecting burned areas in large-scale farmland settings and provides valuable information for the development of future detection algorithms. [ABSTRACT FROM AUTHOR]

In this paper, we introduce the Yosida approximation operator associated with H- monotone operator in Hilbert spaces and prove some of its important properties. In addition, we consider a system of generalized nonlinear variational inclusions involving Yosida approximation operator and establish its equivalence with the fixed point problems using resolvent operator technique. This alternative equivalent formulation is employed to propose an iterative algorithm for solving this system of generalized nonlinear variational inclusions. Further, we discuss the existence of solution and convergence analysis of the proposed iterative algorithm under suitable conditions. Finally, we present a numerical example in support of the results proved and demonstrate the convergence result using MATLAB. [ABSTRACT FROM AUTHOR]

In this paper, we introduce a new iterative algorithm for finding a common solution for variational inclusion problem and fixed point problem in real Hilbert spaces. This method can be implemented more easily without the prior knowledge of the Lipschitz constant of component operators. The algorithm uses variable step-sizes which are updated at each iteration by a simple computation. In additional, weak and strong convergence results of the proposed algorithm are obtained under some mild conditions. Then, we establish the linear rate of convergence for the proposed algorithm. Finally, an example is given to illustrate the convergence of the algorithm. [ABSTRACT FROM AUTHOR]

In this paper, we are interested in the investigation of the problem of finding a common element of the set of fixed points of a total uniformly L-Lipschitzian mapping and the set of solutions of a system of generalized nonlinear variational-like inclusions. To approximate such a point lying in the above two sets, by employing some total uniformly L-Lipschitzian mappings and the notion of P- η -proximal-point mapping, a new iterative scheme is constructed. We apply the notions of graph convergence and P- η -proximal-point mapping and establish a new equivalence relationship between graph convergence and proximal-point mappings convergence of a sequence of P- η -accretive mappings. As an application of the obtained equivalence relationship, the strong convergence and stability of the sequence generated by our proposed iterative algorithm to a common point of the above-mentioned two sets are proved. The final section is devoted to the investigation and analysis of the results given in [Nonlinear Anal. 67(2007), 917–929]. Some comments relating to them are pointed out. These results are new, and improve and generalize many known corresponding results. [ABSTRACT FROM AUTHOR]

In this paper, we present a novel high-order structure-preserving numerical scheme for solving the damped nonlinear space fractional Schrödinger equation (DNSFSE) in two spatial dimensions. The main idea of constructing new algorithm consists of two parts. Firstly, we introduce an auxiliary exponential variable to transform the original DNSFSE into a modified one. The modified DNSFSE subjects to the conservation of mass and energy, which is crucial to develop structure-preserving numerical schemes. Secondly, we construct a high-order numerical differential formula to approximate the Riesz derivative in space, which contributes to a semi-discrete difference scheme for the modified DNSFSE. Combining the semi-discrete scheme with the variant Crank–Nicolson method in time, we can obtain the fully-discrete difference scheme for solving the modified DNSFSE. The advantage of the proposed scheme is that a fourth-order convergent accuracy can be achieved in space while maintaining the conservation of mass and energy. Subsequently, we conduct a detailed study on the boundedness, uniqueness, and convergence of solution for fully-discrete scheme. Furthermore, an improved efficient iterative algorithm is proposed for the fully-discrete scheme, which has the advantage of maintaining the same convergence order as the original difference scheme. Finally, extensive numerical results are reported to further verify the correctness of theoretical analysis and the effectiveness of the proposed numerical algorithm. [ABSTRACT FROM AUTHOR]

The present paper is concerned with exploiting an iterative decoupling algorithm to address the problem of third-order tensor deblurring. The regularized deblurring problem, which is mathematically given by the sum of a fidelity term and a regularization term, is decoupled into an observation fidelity and a denoiser model steps. One basic advantage of the iterative decoupling algorithm is that the deblurring problem is supervised by the efficiency of the denoiser model. Thus, we consider a patch-based weighted low-rank tensor with sparsity prior. Numerical tests to image deblurring are given to demonstrate the efficiency of the proposed decoupling based algorithm. [ABSTRACT FROM AUTHOR]

ObjectiveTo evaluate the image quality and diagnostic performance of AI-assisted iterative algorithm protocols (AIIA) in accelerated fast spin-echo magnetic resonance imaging (MRI) versus standard (SD) fast spin-echo MRI for clinical 3.0 T rapid knee scans.Materials and methodsThe accelerated sequence, which includes fat-suppression proton density-weighted imaging (FS-PDWI), T2-weighted imaging (T2WI), and T1-weighted imaging (T1WI), was used in conjunction with the SD sequence in 61 patients who underwent MRI scans. SD images were processed using standard reconstruction techniques, while accelerated images utilized AIIA reconstruction. Quantitative assessments of image quality were conducted, measuring noise levels, signal-to-noise ratio (SNR) and contrast signal-to-noise ratio (CNR). Additionally, subjective evaluations were performed using a Likert five-point scale to assess image quality.ResultsThe SD group completed the entire knee scan in 466 s, while the AIIA group completed the scan in 312 s. Compared to the SD group, the AIIA group had a noticeably higher SNR of T1WI in the femur and subpatellar fat pad (p = 0.04, 0.001). On the other hand, T2WI femur SNR was noticeably higher in the SD group (p = 0.004). Measurements of SNR, CNR and other noise levels showed no statistically significant changes. Compared to the SD group, the AIIA group had significantly higher subjective image quality scores for every sequence (p 0.05).ConclusionImages processed using AIIA reconstruction were acquired faster while maintaining comparable image quality and diagnostic capability, meeting the requirements for clinical diagnosis.

Abstract Unmanned aerial vehicles (UAVs) offer a new approach to wireless communication, leveraging their high mobility, flexibility, and visual communication capabilities. Ambient backscatter communication enables Internet of Things devices to transmit data by reflecting and modulating ambient radio waves, eliminating the need for additional wireless channels, and reducing energy consumption and cost for sensors. However, passive ambient backscatter communication has limitations such as limited range and poor communication quality. By utilizing UAVs as communication nodes, these limitations can be overcome, expanding the communication range and improving the quality of communication. Although some research has been conducted on combining UAVs and ambient backscatter, several challenges remain. One key challenge is the strong direct link interference in ambient backscatter under UAV conditions, which significantly affects communication quality. In this paper, we propose an intelligent backward and forward straight link interference cancellation algorithm based on NOMA decoding technique to enhance ambient backscatter communication quality under UAV conditions and extract more ambient energy for UAV energy supply. The paper includes theoretical derivation, algorithm description, and simulation analysis to validate the error bit rate of labeled information bits. The results demonstrate that the forward algorithm reduces the error bit rate by approximately 20% under low signal-to-noise ratio (SNR) conditions, while the backward algorithm reduces the error bit rate under high SNR conditions. The combination of the forward and backward algorithms reduces the error bit rate under both high and low SNR conditions. The proposed method contributes to improving the quality of ambient backscatter communication in UAV settings.

The square root is one of the most important basic operations in computers. Based on the parallel carry-free TW-MSD adder, the parallel R4-MSD square root algorithm is proposed and presented. The algorithm is designed and implemented on the protype SD16 of ternary optical computer, which is developed by Shanghai University in 2016. The processes of the R4-MSD square root algorithm is described in detail. The optical experiment of the square root algorithm is presented based on the protype SD16 of ternary optical computer. It is proved that there are at most two square roots for MSD number representations of a positive decimal number within a given precision scope. It takes clock cycles to complete the square root of a MSD number of length n. This algorithm also shows that it requires the same clock cycle for multiple MSD numbers as for a single MSD number with the equal length. It is better than the radix-2 square root for MSD numbers and other embedded systems. Theoretical proof and optical experiments show that the parallel R4-MSD square root algorithm is feasible. It makes full use of the advantages of the ternary optical processor such as huge digits, bit function reconfiguration, and bit-based allocation. [ABSTRACT FROM AUTHOR]

To improve the estimation efficiency of high-dimensional regression problems, penalized regularization is routinely used. However, accurately estimating the model remains challenging, particularly in the presence of correlated effects, wherein irrelevant covariates exhibit strong correlation with relevant ones. This situation, referred to as correlated data, poses additional complexities for model estimation. In this paper, we propose the elastic-net multi-step screening procedure (EnMSP), an iterative algorithm designed to recover sparse linear models in the context of correlated data. EnMSP uses a small repeated penalty strategy to identify truly relevant covariates in a few iterations. Specifically, in each iteration, EnMSP enhances the adaptive lasso method by adding a weighted l 2 penalty, which improves the selection of relevant covariates. The method is shown to select the true model and achieve the l 2 -norm error bound under certain conditions. The effectiveness of EnMSP is demonstrated through numerical comparisons and applications in financial data. [ABSTRACT FROM AUTHOR]

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Unmanned aerial vehicles (UAVs) offer a new approach to wireless communication, leveraging their high mobility, flexibility, and visual communication capabilities. Ambient backscatter communication enables Internet of Things devices to transmit data by reflecting and modulating ambient radio waves, eliminating the need for additional wireless channels, and reducing energy consumption and cost for sensors. However, passive ambient backscatter communication has limitations such as limited range and poor communication quality. By utilizing UAVs as communication nodes, these limitations can be overcome, expanding the communication range and improving the quality of communication. Although some research has been conducted on combining UAVs and ambient backscatter, several challenges remain. One key challenge is the strong direct link interference in ambient backscatter under UAV conditions, which significantly affects communication quality. In this paper, we propose an intelligent backward and forward straight link interference cancellation algorithm based on NOMA decoding technique to enhance ambient backscatter communication quality under UAV conditions and extract more ambient energy for UAV energy supply. The paper includes theoretical derivation, algorithm description, and simulation analysis to validate the error bit rate of labeled information bits. The results demonstrate that the forward algorithm reduces the error bit rate by approximately 20% under low signal-to-noise ratio (SNR) conditions, while the backward algorithm reduces the error bit rate under high SNR conditions. The combination of the forward and backward algorithms reduces the error bit rate under both high and low SNR conditions. The proposed method contributes to improving the quality of ambient backscatter communication in UAV settings. [ABSTRACT FROM AUTHOR]

The present article considers the estimation of functional product surface properties using the results of measuring areal surface texture parameters via morphological filtering. Under this method, a form of measurement data representation is proposed to improve the efficiency of an algorithm for iterating over surface coordinates. It is shown that for wide implementation of areal morphological filtering in metrological practice, it is necessary to create an efficient filtering algorithm. In the work, an algorithm was developed relying on a matrix representation of morphological operations on surface coordinates. Different indexing of the primary surface and structuring element points was introduced. A sphere or flat segment was used as the structuring element. The performance of the developed algorithm is higher than that of some other algorithms due to the fact that all computations are performed by iterating over surface coordinates in a single pass without nested loops. The diagrams of algorithms for the morphological operations of dilation and erosion are given; these operations were used to construct closing and opening filters. Simulations performed for different datasets and a comparison with known morphological filtering algorithms confirmed the high efficiency of the developed algorithm. The obtained results can be applied in the analysis of the functional properties of product surfaces. [ABSTRACT FROM AUTHOR]

This paper focuses on investigating the problem of finding a common element of the set of solutions of a generalized nonlinear implicit variational-like inclusion problem involving an $ (A,\eta) $ (A , η) -maximal m-relaxed monotone mapping in the sense of L.-G.-s.i.p. and the set of fixed points of a total asymptotically nonexpansive mapping. To achieve such a purpose, a new iterative algorithm is constructed. Applying the concepts of graph convergence and generalized resolvent operator associated with an $ (A,\eta) $ (A , η) -maximal m-relaxed monotone mapping in the sense of L.-G.-s.i.p. As an application of the obtained equivalence relationship, the strong convergence of the sequence generated by our proposed iterative algorithm to a point belonging to the intersection of the two sets mentioned above is proved. [ABSTRACT FROM AUTHOR]

In this paper, by the transformation form of the discrete algebraic Riccati equation (DARE), we propose a new inverse-free iterative algorithm to obtain the positive definite solution of the DARE. Furthermore, the monotone convergence is proved and convergence rate analysis is presented for the derived algorithm. Compared with some existing algorithms, numerical examples demonstrate the feasibility and effectiveness of our algorithm. [ABSTRACT FROM AUTHOR]

Objectives. The purpose of this work was to create an effective iterative algorithm for the tomographic reconstruction of objects with large volumes of initial data. Unlike the convolutional projection algorithm, widely used in commercial industrial and medical tomographic devices, algebraic iterative reconstruction methods use significant amounts of memory and typically involve long reconstruction times. At the same time, iterative methods enable a wider range of diagnostic tasks to be resolved where greater accuracy of reconstruction is required, as well as in cases where a limited amount of data is used for sparse-view angle shooting or shooting with a limited angular range.Methods. A feature of the algorithm thus created is the use of a polar coordinate system in which the projection system matrices are invariant with respect to the rotation of the object. This enables a signification reduction of the amount of memory required for system matrices storage and the use of graphics processors for reconstruction. Unlike the simple polar coordinate system used earlier, we used a coordinate system with a dichotomous division of the reconstruction field enabling us to ensure invariance to rotations and at the same time a fairly uniform distribution of spatial resolution over the reconstruction field.Results. A reconstruction algorithm was developed on the basis of the use of partial system matrices corresponding to the dichotomous division of the image field into partial annular reconstruction regions. A 2D and 3D digital phantom was used to show the features of the proposed reconstruction algorithm and its applicability to solving tomographic problems.Conclusions. The proposed algorithm allows algebraic image reconstruction to be implemented using standard libraries for working with sparse matrices based on desktop computers with graphics processors.

Efficient and timely sharing of critical information is crucial for Public Safety (PS) communications, which can be fulfilled using one of the cutting-edge technologies, Device-to-device (D2D) communication. During an emergency, the PS applications should be prioritized over other applications, ensuring the emergency messages reach the first responders in time. Due to its inherent characteristics, the evolved Node Base station will not prioritize or categorize the D2D communication based on its application type, thus treating all applications equally. Further, D2D communication introduces significant interference to cellular users and vice-versa while sharing resources, and it is vital to reduce the impact of these interferences to ensure the Quality of Service for all users in the network. Hence, this article proposes a novel interference management approach to increase the overall sum rate of the system. In addition, the proposed approach also allows more D2D communication in general, particularly PS application-based D2D communication, to be active in the network. As the formulated problem is a Mixed-Integer Non-Linear Programming (MINLP) type of problem, it is split into two sub-problems, namely, Iterative Resource Allocation and Sharing and Iterative Power Optimization to achieve a polynomial time complexity. The theoretical proofs adequately explain the algorithm’s time complexity and convergence property. The simulation results show that the proposed system enhances the overall sum rate by allowing more active PS D2D applications in the network.