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Abstract: In abstract of the paper [A. Rafiq, A note on “A family of methods for solving nonlinear equations”, Appl. Math. Comput. 195 (2008) 819–821] we can find the following sentences. We cite: Ujević et al. introduced a family of methods for solving nonlinear equations. However the main Algorithm 1 put forward by Ujević et al. (p. 7) is wrong. This is the main aim of this note. We also point out some major bugs in the results of Ujević et al. – the end of the citation. Here it is shown that all of the mentioned assertions are not true. In other words, the Algorithm 1 is correct (up to an obvious misprint, which is not mentioned in the above paper) and there are no major bugs in the paper by Ujević et al. In fact, these observations, which will be given in this note, show that the main aim of the paper by Rafiq is wrong. [Copyright &y& Elsevier]

Neural network learning is usually time-consuming since backpropagation needs to compute full gradients and backpropagate them across multiple layers. Despite its success of existing works in accelerating propagation through sparseness, the relevant theoretical characteristics remain under-researched and empirical studies found that they suffer from the loss of information contained in unpropagated gradients. To tackle these problems, this paper presents a unified sparse backpropagation framework and provides a detailed analysis of its theoretical characteristics. Analysis reveals that when applied to a multilayer perceptron, our framework essentially performs gradient descent using an estimated gradient similar enough to the true gradient, resulting in convergence in probability under certain conditions. Furthermore, a simple yet effective algorithm named m emorized s parse b ack p ropagation (MSBP) is proposed to remedy the problem of information loss by storing unpropagated gradients in memory for learning in the next steps. Experimental results demonstrate that the proposed MSBP is effective to alleviate the information loss in traditional sparse backpropagation while achieving comparable acceleration. [ABSTRACT FROM AUTHOR]

The null space pursuit (NSP) algorithm is an operator-based signal separation approach which separates a signal into a set of additive subcomponents using adaptively estimated operators and parameters. In this paper, a new operator termed complex-valued differential (CD) operator is proposed. Combining with the CD operator, this paper proposes NSP-CD algorithm to solve the CD operator-based signal separation problem. The NSP-CD algorithm can separate the multi-component signal into sum of amplitude-modulated and frequency-modulated (AM–FM) signals in the form of A ( t ) exp ( j ) ( ϕ ( t ) ) . The proposed NSP-CD algorithm has many advantages. Firstly, the proposed CD operator can ensure that the AM–FM signal totally lies in the null space of the operator rather than close to the null space that the original used operator may reach. Secondly, compared with the original NSP algorithm, our algorithm provides a more reasonable strategy to update the regularization parameter λ and the leakage factor γ . Finally, we have proved that the proposed algorithm has quadric convergence theoretically. Experiments on both synthetic and real-life signals demonstrate that the NSP-CD algorithm is more robust and effective than other state-of-the-art methods. [ABSTRACT FROM AUTHOR]

This paper considers identification of nonlinear rational systems defined as the ratio of two nonlinear functions of past inputs and outputs. Despite its long history, a globally consistent identification algorithm remains illusive. This paper proposes a globally convergent identification algorithm for such nonlinear rational systems. To the best of our knowledge, this is the first globally convergent algorithm for the nonlinear rational systems. The technique employed is a two-step estimator. Though two-step estimators are known to produce consistent nonlinear least squares estimates if a N consistent estimate can be determined in the first step, how to find such a N consistent estimate in the first step for nonlinear rational systems is nontrivial and is not answered by any two-step estimators. The technical contribution of the paper is to develop a globally consistent estimator for nonlinear rational systems in the first step. This is achieved by involving model transformation, bias analysis, noise variance estimation, and bias compensation in the paper. Two simulation examples and a practical example are provided to verify the good performance of the proposed two-step estimator. [ABSTRACT FROM AUTHOR]

This paper reports the results of a study into a revised algorithm applied to the fatigue life calculation under cyclic multiaxial proportional and non-proportional loading. In contrast to the classical algorithm, which assumes that material parameters in the fatigue criterion are constant, the revised algorithm relates the values of these parameters to the number of cycles to failure. The objectives in this paper include verification of the convergence for the revised algorithm and evaluation of the fatigue life calculation by use of the revised algorithm. Detailed implementations of the multiaxial fatigue criteria by Matake and Papadopoulos are presented for the algorithm. The calculated fatigue lives are compared to the experimental ones for three steel grades: SAE1045, S355J2G and SM45C subjected to cyclic uniaxial and multiaxial proportional and non-proportional loading. It is shown that the revised algorithm provides a sole solution under the proportional and non-proportional loading by application of the Matake and Papadopoulos criteria. A higher convergence between experimental and calculated fatigue life is obtained for the revised algorithm than for the classical one. [ABSTRACT FROM AUTHOR]

Abstract In this paper, we present a two-grid mixed finite element scheme for distributed optimal control problems governed by stationary Stokes equations. In order to avoid the difficulty caused by the symmetry constraint of the stress tensor, we use pseudostress to replace it. The state and co-state are approximated by the lowest order Raviart–Thomas mixed finite element spaces and the control variable is approximated by piecewise constant functions. We first prove that the difference between the interpolation and the numerical solution has superconvergence property for the control u with order h 2. Then, using the postprocessing technique, we derive a second-order superconvergent result for the control u . Next, we construct a two-grid mixed finite element scheme and derive a priori error estimates. Finally, a numerical experiment is presented to verify the theoretical results. [ABSTRACT FROM AUTHOR]

Abstract In this paper, we employ matrix LSQR algorithm to deal with quaternionic least squares problem in order to find the minimum norm solutions with kinds of special structures, and propose a strategy to accelerate convergence rate of the algorithm via right–left preconditioning of the coefficient matrices. We mainly focus on analyzing the minimum norm η -Hermitian solution and the minimum norm η -biHermitian solution to the quaternionic least squares problem, η ∈ { i , j , k }. Other structured solutions also can be obtained using the proposed technique. A number of numerical experiments are performed to show the efficiency of the preconditioned matrix LSQR algorithm. [ABSTRACT FROM AUTHOR]

Abstract In the paper, we present an efficient two grid method for the miscible displacement problem which discretized by mixed finite element methods for the pressure equation and concentration equation at the same time, and then analyzed the error estimate of the two-gird algorithm. At last, the numerical experiment presented confirmed the theoretical results. Compared with the standard mixed finite element methods, this two-grid scheme based on the mixed methods can keep the same convergence order and cost much less work. [ABSTRACT FROM AUTHOR]

In this paper, we propose a norm descent derivative-free algorithm for solving large-scale nonlinear symmetric equations without involving any information of the gradient or Jacobian matrix by using some approximate substitutions. The proposed algorithm is extended from an efficient three-term conjugate gradient method for solving unconstrained optimization problems, and inherits some nice properties such as simple structure, low storage requirements and symmetric property. Under some appropriate conditions, the global convergence is proved. Finally, the numerical experiments and comparisons show that the proposed algorithm is very effective for large-scale problems. [ABSTRACT FROM AUTHOR]

Highlights • Obtain the optimal solution of far rapid cooperative rendezvous in general case. • Design QPSO-SQP and proving the advance of QPSO-SQP. • Solve the complex optimal control problem with 29 variables. Abstract Focused on far-distance rapid cooperative rendezvous between two spacecraft under continuous large thrust, this paper presents a series of artificial intelligence algorithms for fuel and time optimization. The process of far-distance rapid cooperative rendezvous was optimized by a type of hybrid algorithm-integrated Quantum-behaved Particle Swarm Optimization (QPSO) and Sequential Quadratic Programming (SQP). The convergent co-state vectors were obtained by QPSO and subsequently set as the initial values of SQP to search for the exact solutions in a smaller area. Applications of non-coplanar cooperative rendezvous are provided to demonstrate that the QPSO-SQP algorithm has better performance than other popular algorithms in less time consumption, faster convergence rate and highly stable solutions. [ABSTRACT FROM AUTHOR]

The fundamental purpose of the present paper is to apply an effective numerical algorithm based on the mixture of homotopy analysis technique, Sumudu transform approach and homotopy polynomials to obtain the approximate solution of a nonlinear fractional Drinfeld–Sokolov–Wilson equation. The nonlinear Drinfeld–Sokolov–Wilson equation naturally occurs in dispersive water waves. The uniqueness and convergence analysis are shown for the suggested technique. The convergence of the solution is fixed and managed by auxiliary parameter ℏ. The numerical results are shown graphically. Results obtained by the application of the technique disclose that the suggested scheme is very accurate, flexible, effective and simple to use. [ABSTRACT FROM AUTHOR]

In this paper, the simulation results of static var compensator (SVC) for improvement of transient stability in a photo voltaic (PV) system integrated power system are presented. A Proportional Integral Derivative (PID) controller was also incorporated with SVC for contributing necessary damping in case of various disturbance conditions. Here, the dynamic stability of the PV based power system was studied in single machine infinite bus (SMIB) and power system. SVC is integrated with the above PV based power system for damping low frequency oscillations produced due to disturbances in the power system. Further a novel soft computing based approach called quasi-oppositional differential search algorithm (QODSA) was for designing an optimal SVC-PID based damping controller. Initially DSA was applied for optimizing the gains of the controller and finally quasi oppositional learning was incorporated to DSA for obtaining the optimal parameters of SVC-PID controller and also for enhancing the convergence speed. The effectiveness of the proposed technique was also tested with particle swarm optimization (PSO) technique. Transient stability analysis for conventional PID controller, PSO based PID controller, DSA based PID controller and QDSA based PID controller was done analytically as well as quantitatively. It can be observed from the simulation results that the proposed QDSA based PID controller outperforms over other techniques in improving power system stability and also damping low frequency oscillations. [ABSTRACT FROM AUTHOR]

This technical paper presents a distributed continuous-time algorithm to solve multi-agent optimization problem with the team objective being the sum of all local convex objective functions while subject to an equality constraint. The optimal solutions are achieved within fixed time which is independent of the initial conditions of agents. This advantage makes it possible to off-line preassign the settling time according to task requirements. The fixed-time convergence for the proposed algorithm is rigorously proved with the aid of convex optimization and fixed-time Lyapunov theory. Finally, the algorithm is valuated via an example. [ABSTRACT FROM AUTHOR]

In this paper we propose an algorithm to estimate the parameters, including time delay, of continuous time systems based on instrumental variable identification methods. To overcome the multiple local minima of the cost function associated with the estimation of a time delay system, we utilize the useful redundancy technique. Specifically, the cost function is filtered through a set of low-pass filters to improve convexity with the useful redundancy technique exploited to achieve convergence to the global minimum of the optimization problem. Numerical examples are presented to demonstrate the effectiveness of the proposed algorithm. [ABSTRACT FROM AUTHOR]

A novel adaptive frequency-domain system identification method for linear time-invariant systems is proposed in this paper. It finds poles for discrete rational atoms with discrete frequency responses. The theoretical foundation, including adaptive decomposition principle and decomposition convergence rate, is established. The algorithm of the adaptive pursuit is also provided in this paper. [ABSTRACT FROM AUTHOR]

In this paper, a three-term conjugate gradient algorithm is developed for solving large-scale unconstrained optimization problems. The search direction at each iteration of the algorithm is determined by rectifying the steepest descent direction with the difference between the current iterative points and that between the gradients. It is proved that such a direction satisfies the approximate secant condition as well as the conjugacy condition. The strategies of acceleration and restart are incorporated into designing the algorithm to improve its numerical performance. Global convergence of the proposed algorithm is established under two mild assumptions. By implementing the algorithm to solve 75 benchmark test problems available in the literature, the obtained results indicate that the algorithm developed in this paper outperforms the existent similar state-of-the-art algorithms. [ABSTRACT FROM AUTHOR]

In this paper, we extend convergence conditions for the parameter adaptation algorithm, used in discrete-time recursive identification schemes, or in adaptive control. Whereas the classical stability analysis of this algorithm consists in checking the strictly real positiveness of an associated transfer function, we demonstrate that convergence can be obtained even when this condition is not fulfilled, under some assumptions on the algorithm forgetting factors. These results regarding both deterministic and stochastic contexts are obtained by analyzing convergence with a prescribed degree of stability. [ABSTRACT FROM AUTHOR]

Nonlocality and spatial heterogeneity of many practical systems have made fractional differential equations very useful tools in Science and Engineering. However, solving these type of models is computationally demanding. In this paper, we propose an exponential integrator method for space fractional models as an attractive and easy-to-code alternative for other existing second-order exponential integrator methods. This scheme is based on using a real distinct poles discretization for the underlying matrix exponentials. One of the major benefits of the proposed scheme is that the algorithm could be easily implemented in parallel to take advantage of multiple processors for increased computational efficiency. The scheme is established to be second-order convergent; and proven to be robust for nonlinear space fractional reaction–diffusion problems involving non-smooth initial data. Our approach is exhibited by solving a system of two-dimensional problems which exhibits pattern formation and has applications in cell-division. Empirically, super-diffusion processes are displayed by investigating the effect of the fractional power of the underlying Laplacian operator on the pattern formation found in these models. Furthermore, the superiority of our method over competing second order ETD schemes, BDF2 scheme, and IMEX schemes is demonstrated. [ABSTRACT FROM AUTHOR]

It is well known that the support vector machine (SVM) is an effective learning algorithm. The alternating direction method of multipliers (ADMM) algorithm has emerged as a powerful technique for solving distributed optimisation models. This paper proposes a distributed SVM algorithm in a master–slave mode (MS-DSVM), which integrates a distributed SVM and ADMM acting in a master–slave configuration where the master node and slave nodes are connected, meaning the results can be broadcasted. The distributed SVM is regarded as a regularised optimisation problem and modelled as a series of convex optimisation sub-problems that are solved by ADMM. Additionally, the over-relaxation technique is utilised to accelerate the convergence rate of the proposed MS-DSVM. Our theoretical analysis demonstrates that the proposed MS-DSVM has linear convergence, meaning it possesses the fastest convergence rate among existing standard distributed ADMM algorithms. Numerical examples demonstrate that the convergence and accuracy of the proposed MS-DSVM are superior to those of existing methods under the ADMM framework. [ABSTRACT FROM AUTHOR]

Traditional Gaussian estimation of distribution algorithms (EDAs) are confronted with issues that the variable variances decrease fast and the main search direction tends to become perpendicular to the improvement direction of the fitness function, which reduces the search efficiency of Gaussian EDAs (GEDAs) and makes them subject to premature convergence. In this paper, a novel anisotropic adaptive variance scaling (AAVS) technique is proposed to improve the performance of traditional GEDAs and a new GEDA variant named AAVS-EDA is developed. The advantages of AAVS over the existing variance scaling strategies lie in its ability for tuning the variances and main search direction of GEDA simultaneously, which are achieved by anisotropically scaling the variances along different eigendirections based on corresponding landscape characteristics captured by a simple topology-based detection method. Besides, AAVS-EDA also adopts an auxiliary global monitor to ensure its convergence by shrinking all the variances if no improvement is achieved in a generation. The evaluation results on 30 benchmark functions of CEC2014 test suite demonstrate that AAVS-EDA possesses stronger global optimization efficiency than traditional GEDAs. The comparison with other state-of-the-art evolutionary algorithms also shows that AAVS-EDA is efficient and competitive. [ABSTRACT FROM AUTHOR]

Convection-dominated transport phenomenon is important for many applications. In these applications, the transport velocity is often a solution of heterogeneous flow problems, which results to a coupled flow and transport phenomena. In this paper, we consider a coupled flow (Stokes problem) and transport (unsteady convection–diffusion problem) in perforated domains. Perforated domains (see Fig. 1) represent void space outside hard inclusions as in porous media, filters, and so on. We construct a coarse-scale solver based on Generalized Multiscale Finite Element Method (GMsFEM) for a coupled flow and transport. The main idea of the GMsFEM is to develop a systematic approach for computing multiscale basis functions. We use a mixed formulation and appropriate multiscale basis functions for both flow and transport to guarantee a mass conservation. For the transport problem, we use Petrov–Galerkin mixed formulation, which provides a stability. As a first approach, we use the multiscale flow solution in constructing the basis functions for the transport equation. In the second approach, we construct multiscale basis functions for coupled flow and transport without solving global flow problem. The novelty of this approach is to construct a coupled multiscale basis function. Numerical results are presented for computations using offline basis. We also present an algorithm for adaptively adding online multiscale basis functions, which are computed using the residual information. Numerical examples using online GMsFEM show the speed up of convergence. [ABSTRACT FROM AUTHOR]

Solving equations of the form H ( x ) = 0 is usually done by applying iterative methods. The main interest of this paper is to improve the domain of starting points for Steffensen’s method. In general, the accessibility of iterative methods that use divided differences in their algorithms is reduced, since there are difficulties in the choice of starting points to guarantee the convergence of the methods. In particular, by using a decomposition of the operator H and applying a special type of iterative methods, which combine two iterative schemes in the algorithms, we can improve the accessibility of Steffensen’s method. Moreover, we analyze the local convergence of the new iterative method proposed in two cases: when H is differentiable and H is non-differentiable. The dynamical properties show that the method also improves the region of accessibility of Steffensen’s method for non-differentiable operators. So, we present an alternative for the non-applicability of Newton’s method to non-differentiable operators that improves the accessibility of Steffensen’s method. The theoretical results are illustrated with numerical experiments. [ABSTRACT FROM AUTHOR]

In this paper, a novel multilayer backpropagation (BP) neural network model is proposed based on conjugate gradient (CG) method with generalized Armijo search. The presented algorithm requires low memory and performs fast convergent speed in practical applications. One reason is that the constructed conjugate direction guarantees the sufficient descent behavior in minimizing the given objective function. The other stems from the fact that the generalized Armijo method can automatically determine a more suitable learning rate in each training epoch. As a theoretical contribution, two deterministic convergent results, weak and strong convergence, have been detailedly proved under more relaxed assumptions. The weak convergence means that the norm of gradient of the objective function tends to zero. For the strong convergence, it represents that the sequence of weight vectors approaches a fixed point. To support the theoretical results, some illustrated simulations have been done on various benchmark datasets. [ABSTRACT FROM AUTHOR]

In the present paper, we introduce the Stancu type generalisation of Lupaş–Schurer operators based on ( p, q )-integers. We are concerned with the basic convergence of the constructed operators based on Korovkin’s type approximation theorem. Further, we obtain the rate of convergence for the new operators in terms of the modulus of continuity, with the help of functions of Lipschitz class and Peetre’s K-functionals. Then, we present three significant numerical mathematical algorithms. Finally, in order to confirm our theoretical results we obtain error estimation and illustrate the convergence of the ( p, q )-Lupaş–Schurer–Stancu operators to certain functions by using MATLAB. [ABSTRACT FROM AUTHOR]

By applying the hierarchical identification principle, the gradient-based iterative algorithm is suggested for solving the Sylvester conjugate matrix equation. With the real representation of a complex matrix, a new convergence proof is given. The necessary and sufficient conditions for the convergence factor is determined to guarantee the convergence of the algorithm for any initial iterative matrix. Also a conjecture by Wu et al. (2010) is solved. A numerical example is offered to illustrate the effectiveness of the suggested algorithm and verify some conclusions proposed in this paper. [ABSTRACT FROM AUTHOR]

In this paper, convergence capability of the conventional fractional order gradient methods (FOGMs) is analyzed and a new FOGM with guaranteed and faster convergence ability is proposed. In particular, we further consider the case that the derivative order varies between 1 and 2, and give some discussion on how to determine the derivative order in the algorithm settings. Simulation results from a number of numerical examples are provided to illustrate the approaches. [ABSTRACT FROM AUTHOR]

The Congruent Matching Cells (CMC) method was invented at the National Institute of Standards and Technology (NIST) for accurate firearm evidence identification and error rate estimation. The CMC method is based on the principle of discretization. The toolmark image of the reference sample is divided into correlation cells. Each cell is registered to the cell-sized area of the compared image that has maximum surface topography similarity. For each resulting cell pair, one parameter quantifies the similarity of the cell surface topography and three parameters quantify the pattern congruency of the registration position and orientation. An identification (declared match) requires a significant number of CMCs, that is, cell pairs that meet both similarity and pattern congruency requirements. The use of cell correlations reduces the effects of "invalid regions" in the compared image pairs and increases the correlation accuracy. The identification accuracy of the CMC method can be further improved by considering a feature named "convergence," that is, the tendency of the x-y registration positions of the correlated cell pairs to converge at the correct registration angle when comparing same-source samples at different relative orientations. In this paper, the difference of the convergence feature between known matching (KM) and known non-matching (KNM) image pairs is characterized, based on which an improved algorithm is developed for breech face image correlations using the CMC method. Its advantage is demonstrated by comparison with three existing CMC algorithms using four datasets. The datasets address three different brands of consecutively manufactured pistol slides, with significant differences in the distribution overlap of cell pair topography similarity for KM and KNM image pairs. For the same CMC threshold values, the convergence algorithm demonstrates noticeably improved results by reducing the number of false-positive or false-negative CMCs in a comparison. [ABSTRACT FROM AUTHOR]

In this paper, we propose two modified augmented Lagrange multiplier algorithms by mean-value for Toeplitz matrix compressive recovery. In the algorithms, the mean-value modification makes the iteration matrices keep the Toeplitz structure which contributes to reduce the SVD time and CPU time. Numerical experiments show that the proposed algorithms achieve better precision than the augmented Lagrange multiplier method, especially when the matrix E is less sparse. Convergence analysis of the proposed algorithms is also given in detail. [ABSTRACT FROM AUTHOR]

Thermal stress analysis is one of key aspects in mechanical design. Based on the indirect boundary integral equation (BIE) and the radial integration method (RIM), this paper develops a boundary-only element method for the boundary stress analysis of three-dimensional (3D) static thermoelastic problems. A transformation system constructed with the normal and two special tangential vectors is used to regularize the singularity in the indirect BIE. The RIM is then employed to transform the domain integrals arising in both displacement and its derivative integral equations into the equivalent boundary integrals, which results in a pure boundary discretized algorithm. Several numerical experiments are provided to verify the accuracy and convergence of the present approach. [ABSTRACT FROM AUTHOR]

Recently, Smooth Rank Function (SRF) is proposed for matrix completion problem. The main idea of this algorithm is based on a continuous and differentiable approximation of the rank function. However, it need to deal with singular value decomposition of matrix in each iteration, which consumes much time for large matrix. In this paper, by utilizing the tri-factorization of matrix, a fast matrix completion method based on SRF is proposed. Then, based on our fast matrix completion method, a rank adaptive smooth rank function approximation is presented with appropriate rank estimation. We mathematically prove the convergence of the proposed method. Experimental results show that our proposed method improves the running time significantly. Furthermore, our proposed method outperforms other existing matrix completion approaches in most cases. [ABSTRACT FROM AUTHOR]

Abstract: Finding the sparset solution of an underdetermined system of linear equations y=Ax has attracted considerable attention in recent years. Among a large number of algorithms, iterative thresholding algorithms are recognized as one of the most efficient and important classes of algorithms. This is mainly due to their low computational complexities, especially for large scale applications. The aim of this paper is to provide guarantees on the global convergence of a wide class of iterative thresholding algorithms. Since the thresholds of the considered algorithms are set adaptively at each iteration, we call them adaptively iterative thresholding (AIT) algorithms. As the main result, we show that as long as A satisfies a certain coherence property, AIT algorithms can find the correct support set within finite iterations, and then converge to the original sparse solution exponentially fast once the correct support set has been identified. Meanwhile, we also demonstrate that AIT algorithms are robust to the algorithmic parameters. In addition, it should be pointed out that most of the existing iterative thresholding algorithms such as hard, soft, half and smoothly clipped absolute deviation (SCAD) algorithms are included in the class of AIT algorithms studied in this paper. [Copyright &y& Elsevier]

Abstract: Multipoint iterative methods belong to the class of the most efficient methods for solving nonlinear equations. Recent interest in the research and development of this type of methods has arisen from their capability to overcome theoretical limits of one-point methods concerning the convergence order and computational efficiency. This survey paper is a mixture of theoretical results and algorithmic aspects and it is intended as a review of the most efficient root-finding algorithms and developing techniques in a general sense. Many existing methods of great efficiency appear as special cases of presented general iterative schemes. Special attention is devoted to multipoint methods with memory that use already computed information to considerably increase convergence rate without additional computational costs. Some classical results of the 1970s which have had a great influence to the topic, often neglected or unknown to many readers, are also included not only as historical notes but also as genuine sources of many recent ideas. To a certain degree, the presented study follows in parallel main themes shown in the recently published book (Petković et al., 2013) [53], written by the authors of this paper. [Copyright &y& Elsevier]

Highlights: [•] This paper proposes a decomposition algorithm for sparse signal reconstruction. [•] A small quadratic programming problem is solved in each iteration. [•] The convergence of the decomposition algorithm is also shown in this paper. [•] The decomposition method can get a fast convergence for small regularization values. [Copyright &y& Elsevier]

The paper considers the problem of definition of characteristic length parameter and Knudsen number in the calculation of the effective coefficient of thermal conductivity of highly porous fibrous materials. As the characteristic length it is proposed to use the parameter of average distance between fibers instead of the commonly used parameter of the average pore size. We introduced the technique for determining the average distance between fibers in the fibrous highly porous structures with different spatial orientation, volume content, diameter and length of fibers. The technique is based on the direct measurements of the distances between the fibers in representative volume elements (RVE) of fibrous structures. The requirements for the minimum size of the RVE are established. It is shown the convergence of the algorithm whenever we increase the number of measurements in various similar RVE of the same structure. We held the calculations of the average distance between the fibers in the three-dimensional isotropic structures with different volume content and diameter of the fibers. It is shown that the average distance between the fibers is always greater than the average pore size that determined on the basis of geometric methods or based on the known approximate analytical evaluations. It is proposed the modification of a simple analytical formula for the prediction of the average distance between the fibers in the highly porous structures. It is shown that the use of the parameter of average distance between fibers instead of the average pore size leads to the 2–3 times increase of the estimated gas effective thermal conductivity in the pores of the fibrous structure under low pressure. [ABSTRACT FROM AUTHOR]

This paper presents an algorithm for the minimum zone flatness tolerance of a finite point set, which is defined to be the minimum Euclidean distance between two parallel planes that sandwich the point set. The algorithm is based on the observation that the flatness tolerance is equal to the radius of the largest inscribed ball in the convex hull of the Minkowski difference of the point set and itself, which is a symmetric polyhedron with respect to the origin. Then, an iterative procedure is developed to adaptively grow another symmetric polyhedron inside the convex hull of the Minkowski difference such that the radius of its inscribed ball monotonically increases and converges to the flatness tolerance. The algorithm is guaranteed to compute the globally minimum solution within finite iterations. Moreover, there is no need to compute the Minkowski difference or the convex hull of the point set, so the proposed algorithm is very fast and takes only several milliseconds for hundreds of thousands of points on a normal computer, such as a desktop computer with an Intel Xeon 3.70 GHz CPU and 16GB RAM used in this work. [ABSTRACT FROM AUTHOR]

This paper addresses design of an observer-based adaptive fuzzy controller for a class of single-input–single-output (SISO) nonlinear systems with unknown dynamics subject to input nonlinearity and unknown direction. The proposed controller is singularity free. A high-gain observer is designed to estimate the unmeasured states, and the Lipschitz condition for proving boundedness of the estimated states is relaxed. The Nussbaum function is used to handle the unknown virtual control directions and the backstepping technique has been applied for controller design. It is proved that all closed loop signals are semi-globally uniformly ultimately bounded (SGUUB) and the output tracking error converges to a small neighborhood of the origin by choosing the design parameters appropriately. Numerical example illustrates effectiveness of the proposed method even for the system with a change in control direction. [ABSTRACT FROM AUTHOR]

This paper considers the adaptive fuzzy output feedback control design problem for a class of switched nonlinear systems. The considered switched nonlinear systems contain unknown nonlinearities, the switching signals with average dwell time, and without requiring that state variables are available for measurement. Fuzzy logic systems are used to approximate the unknown nonlinearities, and a fuzzy switched state observer is designed to estimate the immeasurable states. In the framework of observer-based output feedback control design technique, and by introducing a command filter into the backstepping design algorithm, a command filter-based adaptive fuzzy backstepping output feedback control scheme is developed. The stability of the closed-loop system and the convergence of the tracking error are proved via average dwell time and multiple Lyapunov function. A numerical example is provided to illustrate the effectiveness of the proposed approach. [ABSTRACT FROM AUTHOR]

Although the bin-normalized frequency domain block LMS (NFBLMS) algorithm has theoretically very fast convergence speed, it suffers from convergence to a biased steady state solution when causality is not met or when the adaptive filter is of deficient length. A modified FBLMS (MFBLMS) algorithm with guaranteed optimal steady state performance has been proposed, but the theoretical analysis on its convergence properties has not been presented. This paper analyzes the convergence behavior of the algorithm by using the theory of asymptotically equivalent matrices. The eigenvalues of the matrix controlling the convergence behavior is proven to have the tendency to be equally distributed, and a theoretical eigenvalue spread is derived based on the first-order autoregressive (AR) signal model, which is significantly lower than that of the time domain LMS (TDLMS) algorithm. Therefore the convergence speed of the MFBLMS is significantly higher than that of the TDLMS algorithm for colored reference signal. Simulations are carried out to validate the convergence behavior predicted from the theoretical analysis. [ABSTRACT FROM AUTHOR]

In this paper, we consider a feasible primal–dual interior point method for linear semidefinite programming problem ( S D P ) based on Alizadeh–Haeberly–Overton ( AHO ) direction (Monteiro, 1997). Firstly, and by a new and simple technique, we establish the existence and uniqueness of optimal solution of the perturbed problem ( S D P ) μ and its convergence to optimal solution of ( S D P ) . Next, we present new different alternatives to calculate the displacement step. After, we establish the convergence of the obtained algorithm and we show that its complexity is O ( n ln [ ε − 1 ( 〈 X 0 , S 0 〉 ) ] ) . Finally, we present some numerical simulations which show the effectiveness of the algorithm developed in this work. [ABSTRACT FROM AUTHOR]

The conventional SIMPLE algorithm for the pressure–velocity coupling has been adopted by many commercial and non-commercial CFD codes. It encounters convergence problem when it is used to solve unsteady natural convection flows with zero-isothermal compressibility. In this paper, a modified version of this algorithm is proposed to remedy this drawback. The modification includes updating of the density at each time step based on its value at the previous time step to satisfy the continuity equation. As an example of utilizing the modified SIMPLE algorithm, the unsteady natural convection in a rectangular cavity with isothermal vertical walls and adiabatic horizontal walls was computed. Physically consistent results were obtained. [ABSTRACT FROM AUTHOR]

ℓ p regularization has been a popular pruning method for neural networks. The parameter p was usually set as 0 < p ≤ 2 in the literature, and practical training algorithms with ℓ 0 regularization are lacking due to the NP-hard nature of the ℓ 0 regularization problem; however, the ℓ 0 regularization tends to produce the sparsest solution, corresponding to the most parsimonious network structure which is desirable in view of the generalization ability. To this end, this paper considers an online gradient training algorithm with smoothing ℓ 0 regularization (OGTSL0) for feedforward neural networks, where the ℓ 0 regularizer is approximated by a series of smoothing functions. The underlying principle for the sparsity of OGTSL0 is provided, and the convergence of the algorithm is also theoretically analyzed. Simulation examples support the theoretical analysis and illustrate the superiority of the proposed algorithm. [ABSTRACT FROM AUTHOR]

As an important extension to sparsity, Block Structured Sparsity (BSS) has been widely investigated and a large set of algorithms have been designed to recover signals with BSS. In this paper, a dynamic system is proposed to recover signals with BSS, namely D-BSS. Particularly, D-BSS turns to exploiting the dynamic systems governed by an ℓ 2 , 1 norm constraint. It can be proved that the equilibrium of D-BSS is equivalent to optimum of traditional BSS algorithms, e.g., Group-lasso. Simulation results are given to illustrate the desirable performance of the D-BSS system, especially the improvement of convergence rate. [ABSTRACT FROM AUTHOR]

The alternating direction method with multipliers (ADMM) has been one of most powerful and successful methods for solving a two-block linearly constrained convex minimization model whose objective function is the sum of two functions without coupled variables. It is known that the numerical efficiency is inherited for a large number of applications, but the convergence is not guaranteed if the ADMM is directly extended to a multiple-block convex minimization model whose objective function has more than two functions. This viewpoint was in fact the motivation for developing efficient algorithms that cannot only preserve the numerical advantages of the direct extension of ADMM but also guarantee convergence. One way is to correct the output of the direct extension of ADMM slightly via a simple correction step, and the other is to employ a simple proximal to solve inexactly each subproblem in the direct extension of ADMM. In this paper, in order to solve the multi-block separable convex minimization model efficiently, we present a method which is a combination of the above two ways, that is, we first solve each subproblem with a simple proximal, then we correct the output via a simple correction step. Theoretically, we derive global convergence results for this method and establish a worst-case O ( 1 / k ) iteration complexity. Numerically, the efficiency of this method can be showed by testing the problem of recovering low-rank and sparse components of matrices from incomplete and noisy observation. [ABSTRACT FROM AUTHOR]

Abstract: Very recently, Yao et al. (2010) [4] proposed a hybrid iterative algorithm. Under the parameter sequences satisfying some quite restrictive conditions, they derived a strong convergence theorem in a Hilbert space. In this paper, under the weaker conditions, we prove the strong convergence of the sequence generated by their iterative algorithm to a common fixed point of an infinite family of nonexpansive mappings, which solves a variational inequality. An appropriate example, such that all conditions of this result that are satisfied and that other conditions are not satisfied, is provided. Moreover, the method of our paper is different from the method in Yao et al. (2010) [4]. [Copyright &y& Elsevier]