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Particle-based methods based on material models using spheres can provide good approximations for many physical phenomena at both the micro and macroscales. The point of departure for the simulations, in general, is a dense arrangement of spherical particles (sphere pack) inside a given container. For generic domains, the generation of a sphere pack may be complex and time-consuming, especially if the pack must comply with a prescribed sphere size distribution and the stability requirements of the simulation. The primary goal of this paper is to present an efficient algorithm that is capable of producing packs with millions of spheres following a statistical sphere size distribution inside complex arbitrary domains. This algorithm uses a new strategy to ensure that the sphere size distribution is preserved even when large particles are rejected in the growing process. The paper also presents numerical results that enable an evaluation of the proposed algorithm. [ABSTRACT FROM AUTHOR]

By applying the hierarchical identification principle, the gradient-based iterative algorithm is suggested to solve a class of complex matrix equations. With the real representation of a complex matrix as a tool, the sufficient and necessary conditions for the convergence factor are determined to guarantee that the iterative solutions given by the proposed algorithm converge to the exact solution for any initial matrices. Also, we solve the problem which is proposed by Wu et al. (2010). Finally, some numerical examples are provided to illustrate the effectiveness of the proposed algorithms and testify the conclusions suggested in this paper. [ABSTRACT FROM AUTHOR]

Cyclic pentadiagonal matrices with Toeplitz structure have received tremendous attention in recent years. In the current paper, we present a block upper triangular transformation of the cyclic pentadiagonal Toeplitz matrices. By using the transformation, the determinant of an n -by- n cyclic pentadiagonal Toeplitz matrix can be readily evaluated since one just needs to compute the determinant of a 4-by-4 matrix obtained from the transformation. In addition, an efficient numerical algorithm of O ( n ) is derived for computing n th order cyclic pentadiagonal Toeplitz determinants. Some numerical experiments are given to show the performance of the proposed algorithm. [ABSTRACT FROM AUTHOR]

Abstract: This paper discusses a numerical subgrid resolution approach for solving the Stokes–Brinkman system of equations, which is describing coupled flow in plain and in highly porous media. Various scientific and industrial problems are described by this system, and often the geometry and/or the permeability vary on several scales. A particular target is the process of oil filtration. In many complicated filters, the filter medium or the filter element geometry are too fine to be resolved by a feasible computational grid. The subgrid approach presented in this paper is aimed at describing how these fine details are accounted for by solving auxiliary problems in appropriately chosen grid cells on a relatively coarse computational grid. This is done via a systematic and careful procedure of modifying and updating the coefficients of the Stokes–Brinkman system in chosen cells. This numerical subgrid approach is motivated from one side from homogenization theory, from which we borrow the formulations for the so-called cell problem, and from the other side from the numerical upscaling approaches, such as Multiscale Finite Volume, Multiscale Finite Element, etc. Results on the algorithm’s efficiency, both in terms of computational time and memory usage, are presented. Comparison of the full fine grid solution (when possible) of the Stokes–Brinkman system with the subgrid solution of the upscaled Stokes–Brinkman system (including effective permeabilities for the quasi-porous cells), are presented in order to evaluate the accuracy and the efficiency. Advantages and limitations of the considered subgrid approach are discussed. [Copyright &y& Elsevier]

Abstract: This paper studies a group of basic state reduction based dynamic programming (DP) algorithms for the multi-objective 0–1 knapsack problem (MKP), which are related to the backward reduced-state DP space (BRDS) and forward reduced-state DP space (FRDS). The BRDS is widely ignored in the literature because it imposes disadvantage for the single objective knapsack problem (KP) in terms of memory requirements. The FRDS based DP algorithm in a general sense is related to state dominance checking, which can be time consuming for the MKP while it can be done efficiently for the KP. Consequently, no algorithm purely based on the FRDS with state dominance checking has ever been developed for the MKP. In this paper, we attempt to get some insights into the state reduction techniques efficient to the MKP. We first propose an FRDS based algorithm with a local state dominance checking for the MKP. Then we evaluate the relative advantage of the BRDS and FRDS based algorithms by analyzing their computational time and memory requirements for the MKP. Finally different combinations of the BRDS and FRDS based algorithms are developed on this basis. Numerical experiments based on the bi-objective KP instances are conducted to compare systematically between these algorithms and the recently developed BRDS based DP algorithm as well as the existing FRDS based DP algorithm without state dominance checking. [Copyright &y& Elsevier]

Abstract: This paper continues the theme of the recent work Chen et al. (2008) , in which fast collocation methods are introduced for solving ill-posed Fredholm integral equations of the first kind. We develop in this paper multilevel augmentation algorithms, which lead to fast solutions of the discrete equations resulting from fast collocation methods. Regularization parameter choice strategies are given for proposed methods. The theoretical analysis and numerical experiments illustrate the accuracy and efficiency of the algorithm. [Copyright &y& Elsevier]

Abstract: In this paper, we extend the classical economic order quantity model to allow for not only a function of price-dependent and time-varying demand but also fluctuating unit purchasing cost. The joint replenishment problem is subject to continuous decay and a general partial backlogging rate. The objective is to find the optimal replenishment number, time scheduling and periodic selling price to maximize the discounted total profit. An effective search procedure is provided to find the optimal solution by employing the properties derived in this paper and particle swarm optimization algorithm. Several numerical examples are used to illustrate the features of the proposed model. [ABSTRACT FROM AUTHOR]

Abstract: Preconditioners based on various multilevel extensions of two-level finite element methods (FEM) lead to iterative methods which often have an optimal order computational complexity with respect to the number of degrees of freedom of the system. Such methods were first presented in [O. Axelsson, P.S. Vassilevski, Algebraic multilevel preconditioning methods I, Numer. Math. 56 (1989) 157–177; O. Axelsson, P.S. Vassilevski, Algebraic multilevel preconditioning methods II, SIAM J. Numer. Anal. 27 (1990) 1569–1590] on (recursive) two-level splittings of the finite element space. The key role in the derivation of optimal convergence rate estimates is played by the constant in the so-called strengthened Cauchy–Bunyakowski–Schwarz (CBS) inequality, associated with the angle between the two subspaces of the splitting. More precisely, the value of the upper bound for is a part of the construction of various multilevel extensions of the related two-level methods. In this paper algebraic two-level and multilevel preconditioning algorithms for second-order elliptic boundary value problems are constructed, where the discretization is done using Rannacher–Turek non-conforming rotated bilinear finite elements on quadrilaterals. An important point to make is that in this case the finite element spaces corresponding to two successive levels of mesh refinement are not nested in general. To handle this, a proper two-level basis is required to enable us to fit the general framework for the construction of two-level preconditioners for conforming finite elements and to generalize the method to the multilevel case. The proposed variants of the hierarchical two-level basis are first introduced in a rather general setting. Then, the parameters involved are studied and optimized. The major contribution of the paper is the derived estimates of the constant in the strengthened CBS inequality which is shown to allow the efficient multilevel extension of the related two-level preconditioners. Representative numerical tests well illustrate the optimal complexity of the resulting iterative solver. [Copyright &y& Elsevier]

In this paper, we present the error analysis of a new transformation for multiple zeros finding without calculating derivatives, which is a kind of version proposed in a recent paper of this journal, see [1]. We prove that the new derivative-free transformation could succeed in the maximum accuracy that is attainable at fixed precision of computation and preserves the order of convergence of the iteration method in the case of multiple zeros and show the advantage of this new transformation, compared with the other ones. [Copyright &y& Elsevier]

In this paper, we present two novel symbolic computational algorithms to solve periodic pentadiagonal (PP) linear systems. These two algorithms are based on a special matrix decomposition and the use of any fast pentadiagonal linear solver, respectively. Some numerical examples are given in order to demonstrate the performance of the proposed algorithms and their competitiveness with existing algorithms. All of the experiments are performed on a computer workstation with the aid of programs written in MATLAB. [ABSTRACT FROM AUTHOR]

In this paper we consider a four-dimensional bioreactor model, describing an anaerobic digestion process of wastewater treatment and biogas production. We propose a simple and practically realizable approach for global asymptotic stabilization of the model and for maximizing the biogas flow rate; the latter is achieved by using a numerical extremum seeking algorithm. [ABSTRACT FROM AUTHOR]

Abstract: We describe a method that computes the number of roots of a polynomial inside a region bounded by the curve , with an analysis of its computational cost. It is based on the number of roots being the same as the winding number of . While the usual methods for computing the winding number involve numerical integration, in this paper we use a geometrical construction. We show its correctness without referring to global information about (like its Lipschitz constant on ). The analysis of its cost is based on the distance from the roots to , expressed using a condition number suitably defined. The method can be used in a divide-and-conquer root-finding algorithm. [Copyright &y& Elsevier]

Abstract: This paper is focused on the numerical solution of elliptic equations with discontinuous coefficients. In particular, the design of efficient geometric multigrid methods for cell-centered finite volume schemes for this kind of problems is dealt with. In this work we propose a block-wise multigrid algorithm on semi-structured triangular grids for solving piecewise constant diffusivity problems on relatively complex domains. Appropriate novel smoothers for cell-centered discretizations are considered on each structured patch of the mesh. The difficulties appearing when highly varying coefficients occur are overcome by the use of a modified Galerkin coarse grid approximation. Numerical experiments are presented to illustrate the good behavior of the proposed multigrid method which achieves an -independent convergence rate. [Copyright &y& Elsevier]

Abstract: The paper is devoted to the computational time-domain formulation of linear viscoelastic systems submitted to a nonstationary stochastic excitation and in the presence of model uncertainties which are modeled in the framework of the probability theory. The objective is to introduce and to develop an adapted and complete formulation of such a problem in the context of computational mechanics. A reduced-order model in the time domain with stochastic excitation is derived from the computational model. For the reduced-order model, the stochastic modeling of both computational model-parameter uncertainties and modeling errors is carried out using the nonparametric probabilistic approach and the random matrix theory. We present a new formulation of model uncertainties to construct the random operators for viscoelastic media. We then obtained a linear Stochastic Integro-Differential Equation (SIDE) with random operators and with a stochastic nonhomogeneous part (stochastic excitation). A time discretization of this SIDE is proposed. In a first step, the SIDE is transformed to a linear Itô Stochastic Differential Equation (ISDE) with random operators. Then the ISDE is discretized using an extension of the Störmer–Verlet scheme which is a particularly well adapted algorithm for long-time good behavior of the numerical solution. Finally, for the stochastic solver and statistical estimations of the random responses, we propose to use the Monte Carlo simulation for Gaussian and non-Gaussian excitations. [Copyright &y& Elsevier]

Abstract: This paper investigates the use of multidimensional scaling in the evaluation of fractional system. Several algorithms are analysed based on the time response of the closed loop system under the action of a reference step input signal. Two alternative performance indices, based on the time and frequency domains, are tested. The numerical experiments demonstrate the feasibility of the proposed visualization method. [Copyright &y& Elsevier]

Abstract: Data compression via the Huffman algorithm, which is a data compression technique, is the most efficient technique between single symbol data compression techniques. This algorithm is counted among statistical data compression techniques. Many efforts have been made for optimizing this technique and some algorithms have been presented, too. One of these algorithms is the ACW algorithm which is presented by Hussein Al-Bahadili et al. At first, they used the Huffman algorithm and then used the results of the Huffman algorithm as the input of their algorithm to calculate the optimum character wordlength. So, they decreased the stored characters via increasing the character wordlength for doing the compression. In this paper, we examined and criticized the ACW algorithm and presented some of its weaknesses via suitable counterexamples. At the end, it was concluded that the optimum character wordlength can never be calculated by extant techniques. [Copyright &y& Elsevier]

Abstract: In this paper, we present a numerical approach for solving the system of multi-pantograph equations with mixed conditions. This system is usually difficult to solve analytically. By expanding the approximate solutions by means of the Bessel functions of first kind with unknown coefficients, the proposed approach consists of reducing the problem to a linear algebraic equation system. The unknown coefficients of the Bessel functions of first kind are computed using the matrix operations of derivatives together with the collocation method. An error estimation is given. The reliability and efficiency of the proposed scheme are demonstrated by some numerical examples. All of the numerical computations have been performed on a computer with the aid of a program written in Matlab. [Copyright &y& Elsevier]

Abstract: In this paper, we develop new numeric modified Adomian decomposition algorithms by using the Wazwaz–El-Sayed modified decomposition recursion scheme, and investigate their practicality and efficiency for several nonlinear examples. We show how we can conveniently generate higher-order numeric algorithms at will by this new approach, including, by using examples, 12th-order and 20th-order numeric algorithms. Furthermore, we show how we can achieve a much larger effective region of convergence using these new discrete solutions. We also demonstrate the superior robustness of these numeric modified decomposition algorithms including a 4th-order numeric modified decomposition algorithm over the classic 4th-order Runge–Kutta algorithm by example. The efficiency of our subroutines is guaranteed by the inclusion of the fast algorithms and subroutines as published by Duan for generation of the Adomian polynomials to high orders. [Copyright &y& Elsevier]

Abstract: In this paper, we present an efficient algorithm to compute the whole set of numerical semigroups with a given Frobenius number . The methodology is based on the construction of a partition of that set by a congruence relation. It is proven that each class in the partition contains exactly one irreducible and one homogeneous numerical semigroup, and from those two elements the whole class can be reconstructed. An alternative encoding of a numerical semigroup, its Kunz-coordinates vector, is used to propose a simple methodology to enumerate the desired set by manipulating a lattice polytope of 0–1 vectors and solving certain integer programming problems over it. [Copyright &y& Elsevier]

Abstract: A DoS attack can be regarded as an attempt of attackers to prevent legal users from gaining a normal network service. The TCP connection management protocol sets a position for a classic DoS attack, namely, the SYN flood attack. In this attack some sources send a large number of TCP SYN segments, without completing the third handshake step to quickly exhaust connection resources of the under attack system. This paper models the under attack server by using the queuing theory in which attack requests are recognized based on their long service time. Then it proposes a framework in which the defense issue is formulated as an optimization problem and employs the particle swarm optimization (PSO) algorithm to optimally solve this problem. PSO tries to direct the server to an optimum defense point by dynamically setting two TCP parameters, namely, maximum number of connections and maximum duration of a half-open connection. The simulation results show that the proposed defense strategy improves the performance of the under attack system in terms of rejection probability of connection requests and efficient consumption of buffer space. [Copyright &y& Elsevier]

Abstract: The performance of an optimization tool is largely determined by the efficiency of the search algorithm used in the process. The fundamental nature of a search algorithm will essentially determine its search efficiency and thus the types of problems it can solve. Modern metaheuristic algorithms are generally more suitable for global optimization. This paper carries out extensive global optimization of unconstrained and constrained problems using the recently developed eagle strategy by Yang and Deb in combination with the efficient differential evolution. After a detailed formulation and explanation of its implementation, the proposed algorithm is first verified using twenty unconstrained optimization problems or benchmarks. For the validation against constrained problems, this algorithm is subsequently applied to thirteen classical benchmarks and three benchmark engineering problems reported in the engineering literature. The performance of the proposed algorithm is further compared with various, state-of-the-art algorithms in the area. The optimal solutions obtained in this study are better than the best solutions obtained by the existing methods. The unique search features used in the proposed algorithm are analyzed, and their implications for future research are also discussed in detail. [Copyright &y& Elsevier]

Abstract: In this paper, we present a dynamic programming (DP) algorithm for the multi-objective 0–1 knapsack problem (MKP) by combining two state reduction techniques. One generates a backward reduced-state DP space (BRDS) by discarding some states systematically and the other reduces further the number of states to be calculated in the BRDS using a property governing the objective relations between states. We derive the condition under which the BRDS is effective to the MKP based on the analysis of solution time and memory requirements. To the authors’ knowledge, the BRDS is applied for the first time for developing a DP algorithm. The numerical results obtained with different types of bi-objective instances show that the algorithm can find the Pareto frontier faster than the benchmark algorithm for the large size instances, for three of the four types of instances conducted in the computational experiments. The larger the size of the problem, the larger improvement over the benchmark algorithm. Also, the algorithm is more efficient for the harder types of bi-objective instances as compared with the benchmark algorithm. [Copyright &y& Elsevier]

Abstract: This paper aims at presenting an approach for analyzing finite-source retrial systems with servers subject to breakdowns and repairs, using Generalized Stochastic Petri Nets (GSPNs). This high-level formalism allows a simple representation of such systems with different breakdown disciplines. From the GSPN model, a Continuous Time Markov Chain (CTMC) can be automatically derived. However, for multiserver retrial systems with unreliable servers, the models may have a huge state space. Using the GSPN model as a support, we propose an algorithm for directly computing the infinitesimal generator of the CTMC without generating the reachability graph. In addition, we develop the formulas of the main stationary performance and reliability indices, as a function of the number of servers, the size of the customer source and the stationary probabilities. Through numerical examples, we discuss the effect of the system parameters and the breakdown disciplines on performance. [Copyright &y& Elsevier]

Abstract: In this paper an attempt is made to extend some standard results in set theory on the basis of soft set relations. Antisymmetric relation and transitive closure of a soft set relation are introduced and an analogue of Warshall’s algorithm is proposed for calculating the transitive closure of a soft set relation. Ordering on a soft set is defined and some set theoretical results based on this are proved. [Copyright &y& Elsevier]

Abstract: We study an on-line machine covering problem, in which jobs arrive one by one and their processing times are known upon their arrival, and jobs are allowed to migrate between machines when a new job is added in the system. However, the total processing time of migration induced by an incoming job is bounded by a constant factor times the processing time of the incoming job. The objective is to maximize the minimum machine load. In this paper, we present an on-line algorithm with competitive ratio 6/5 for the two identical machines case with . Moreover, the presented on-line algorithm is only a local migration, that is, when one job is assigned to machine , only the jobs on machine are allowed to migrate. We also show that the provided algorithm is a best possible on-line algorithm in the sense of local migration. [Copyright &y& Elsevier]

Abstract: This paper deals with an inverse problem of determining a source term in the one-dimensional fractional advection–dispersion equation (FADE) with a Dirichlet boundary condition on a finite domain, using final observations. On the basis of the shifted Grünwald formula, a finite difference scheme for the forward problem of the FADE is given, by means of which the source magnitude depending upon the space variable is reconstructed numerically by applying an optimal perturbation regularization algorithm. Numerical inversions with noisy data are carried out for the unknowns taking three functional forms: polynomials, trigonometric functions and index functions. The reconstruction results show that the inversion algorithm is efficient for the inverse problem of determining source terms in a FADE, and the algorithm is also stable for additional data having random noises. [Copyright &y& Elsevier]

Abstract: In this paper, an algorithm for approximate calculation of the attainable sets of nonlinear control systems with integral constraint on controls is presented. A numerical example of the computer application of this algorithm is also given. [Copyright &y& Elsevier]

Abstract: Recently data stream has been extensively explored due to its emergence in a great deal of applications such as sensor networks, web click streams and network flows. One of the most important challenges in data streams is concept change where data underlying distributions change from time to time. A vast majority of researches in the context of data stream mining are devoted to labeled data, whereas, in real word human practice label of data are rarely available to the learning algorithms. Moreover, most of the methods that detect changes in unlabeled data stream merely deal with numerical data sets, and also, they are facing considerable difficulty when dimension of data tends to increase. In this paper, we present a Precise Statistical approach for Concept Change Detection in unlabeled data streams, which, abbreviated as PSCCD, detects changes using an exchangeable test. This hypothesis test is driven from a martingale which is based on Doob’s Maximal Inequality. The advantages of our approach are three fold. First, it does not require a sliding window on the data stream whose size is a well-known challenging issue; second, it works well in multi-dimensional data stream, and last but not the least, it is applicable to different types of data including categorical, numerical and mixed-attribute data streams. To explore the advantages of our approach, quite a lot of experiments with different settings and specifications are conducted. The obtained results are very promising. [Copyright &y& Elsevier]

Abstract: In this paper, we propose a new, fast, and stable hybrid numerical method for multiphase image segmentation using a phase-field model. The proposed model is based on the Allen–Cahn equation with a multiple well potential and a data-fitting term. The model is computationally superior to the previous multiphase image segmentation via Modica-Mortola phase transition and a fitting term. We split its numerical solution algorithm into linear and a nonlinear equations. The linear equation is discretized using an implicit scheme and the resulting discrete system of equations is solved by a fast numerical method such as a multigrid method. The nonlinear equation is solved analytically due to the availability of a closed-form solution. We also propose an initialization algorithm based on the target objects for the fast image segmentation. Finally, various numerical experiments on real and synthetic images with noises are presented to demonstrate the efficiency and robustness of the proposed model and the numerical method. [Copyright &y& Elsevier]

Abstract: This paper explores the problems of generalized center conditions and integrability of resonant infinity for a complex polynomial differential system. The method is based on converting resonant infinity into an elementary singular point by a homeomorphic transformation. The calculation of generalized singular point quantities is an effective way of finding necessary conditions for integrable systems. A new recursive algorithm for computing generalized singular point quantities at the origin of the transformed system is derived. At the same time, a necessary and sufficient condition for resonant infinity to be a generalized complex center is presented. As an application of the new recursive algorithm, the generalized center conditions for resonant infinity for a class of cubic systems are discussed. To the best of our knowledge, this is the first time that the generalized center problem has been considered for resonant infinity. [Copyright &y& Elsevier]

Abstract: In this paper, the robust control problem of uncertain complex delayed dynamical networks with non-identical nodes is investigated. The dynamic output feedback controllers are designed to ensure robustly global stability and a smaller prescribed disturbance attenuation level for the resulting closed-loop systems. The controller design problem can be solved by a cone complementary linearization algorithm involving linear matrix inequality (LMI) conditions. A numerical example is given to illustrate the effectiveness of the proposed method. [Copyright &y& Elsevier]

Abstract: In this paper, we present a new symmetric rank-one (SR1) method for the solution of unconstrained optimization problems. The proposed method involves an algorithm in which the usual SR1 Hessian is updated a number of times in a way to be specified in some iterations, to improve the performance of the Hessian approximation. In particular, we discuss how to consider a criterion for indicating at each iteration whether it is necessary to employ extra updates. However it is well known that there are some theoretical difficulties when applying the SR1 update. Even for a current positive definite Hessian approximation, it is possible that the SR1 update may not be defined or the SR1 update may not preserve positive definiteness at some iterations. We then employ a restarting procedure that guarantees that updated matrices will be well-defined while preserving positive definiteness of updates. Numerical results support these theoretical considerations. They show that the implementation of the SR1 method using extra updating techniques improves the performance of the SR1 method substantially for a number of test problems from the literature. [Copyright &y& Elsevier]

Abstract: A novel modified differential evolution algorithm (NMDE) is proposed to solve constrained optimization problems in this paper. The NMDE algorithm modifies scale factor and crossover rate using an adaptive strategy. For any solution, if it is at a standstill, its own scale factor and crossover rate will be adjusted in terms of the information of all successful solutions. We can obtain satisfactory feasible solutions for constrained optimization problems by combining the NMDE algorithm and a common penalty function method. Experimental results show that the proposed algorithm can yield better solutions than those reported in the literature for most problems, and it can be an efficient alternative to solving constrained optimization problems. [Copyright &y& Elsevier]

Abstract: Equations with box constraints are applied in many fields, for example the complementarity problem. After studying the existing methods, we find that quadratic convergence of majority algorithms is based on the solvability of the equations. But whether the equations are solvable is previously unknown. So, it is necessary to design an algorithm which has fast quadratic convergence. The quadratic convergence does not depend on the solvability of the equations. In this paper, we propose a new method for solving equations. The global and local quadratic convergence of the proposed algorithm are established under some suitable assumptions. We apply the proposed algorithm to a class of stochastic linear complementarity problems. Numerical results show that our method is valid. [Copyright &y& Elsevier]

Abstract: In this paper, we present an new approach to construct the so-called shape preserving interpolation curves. The basic idea is first to approximate the set of interpolated points with a class of MQ quasi-interpolation operators and then pass through the set with the use of multivariate interpolation by using compactly supported radial basis functions. This approach possesses the advantages of certain shape preserving and good approximation behaviors. The proposed algorithm is easy to implement. [Copyright &y& Elsevier]

Abstract: According to the hierarchical identification principle, a hierarchical gradient based iterative estimation algorithm is derived for multivariable output error moving average systems (i.e., multivariable OEMA-like models) which is different from multivariable CARMA-like models. As there exist unmeasurable noise-free outputs and unknown noise terms in the information vector/matrix of the corresponding identification model, this paper is, by means of the auxiliary model identification idea, to replace the unmeasurable variables in the information vector/matrix with the estimated residuals and the outputs of the auxiliary model. A numerical example is provided. [ABSTRACT FROM AUTHOR]

Abstract: In this paper a new approach combining the features of the homotopy concept with an efficient computational algorithm which provides a simple and rigorous procedure to control the convergence of the solution is proposed to find accurate analytical explicit solutions for some oscillators with discontinuities and a fractional power restoring force which is proportional to . A very fast convergence to the exact solution was proved, since the second-order approximation lead to very accurate results. Comparisons with numerical results are presented to show the effectiveness of this method. Four numerical applications prove the accuracy of the method, which works very well for the whole range of initial amplitudes. The obtained results prove the validity and efficiency of the method, which can be easily extended to other strongly nonlinear problems. [ABSTRACT FROM AUTHOR]

Abstract: The block Arnoldi method is one of the most commonly used techniques for large eigenproblems. In this paper, we exploit certain modified Ritz vectors to take the place of Ritz vectors in the thick-restarted block Arnoldi algorithm, and propose a modified thick-restarted block Arnoldi algorithm for large eigenproblems. We then consider how to periodically combine the refined subspace iterative method with the modified thick-restarting block Arnoldi algorithm for computing a few dominant eigenpairs of a large matrix. The resulting algorithm is called a Subspace-Block Arnoldi algorithm. Numerical experiments show the efficiency of our new algorithms. [Copyright &y& Elsevier]

Abstract: In this paper we propose a robust clustering method for handling -type fuzzy numbers. The proposed method based on similarity measures is not necessary to specify the cluster number and initials. Several numerical examples demonstrate the effectiveness of the proposed robust clustering method, especially robust to outliers, different cluster shapes and initial guess. We then apply this algorithm to three real data sets. These are Taiwanese tea, student data and patient blood pressure data sets. Because tea evaluation comes under an expert subjective judgment for Taiwanese tea, the quality levels are ambiguity and imprecision inherent to human perception. Thus, -type fuzzy numbers are used to describe these quality levels. The proposed robust clustering method successfully establishes a performance evaluation system to help consumers better understand and choose Taiwanese tea. Similarly, -type fuzzy numbers are also used to describe data types for student and patient blood pressure data. The proposed method actually presents good clustering results for these real data sets. [Copyright &y& Elsevier]

Abstract: The stability structure for lattice Boltzmann schemes has been introduced in Banda et al. (2006) , Junk and Yong (2007) to analyze the stability of numerical algorithms. The first purpose of this paper is to discuss the stability structure from the perspective of matrix analysis. Its second goal is to illustrate and apply the results to different classes of lattice Boltzmann collision operators. In particular we formulate an equivalence condition–just recently also reported in Yong (2008) –that guarantees the existence of a pre-stability structure. It is then illustrated by several examples, how this equivalence condition can be effectively employed for the systematic verification and construction of stable collision operators. Finally, we point out some shortcomings of the stability structure approach arising in certain cases. [Copyright &y& Elsevier]

Abstract: In this paper, an inversion algorithm for a banded matrix is presented. The twisted decompositions of a banded matrix are given first; then the inverse of the matrix is obtained, one column at time. The method is about two times faster than the standard method based on the decomposition, as is shown with the analysis of computing complexity and the numerical experiments. [Copyright &y& Elsevier]

Abstract: The standard 2D wavelet transform (WT) has been an effective tool in image processing. In recent years, many new transforms have been proposed successively, such as curvelets, bandlets, directional wavelet transform etc, which inherit the merits of the standard WT, and are more adequate at the 2D image processing tasks. Intuitively, it seemed that applying these novel tools to edge detection should acquire finer performance. In this paper, we propose an edge detection approach based on directional wavelet transform which retains the separable filtering and the simplicity of computations and filter design from the standard 2D WT. In addition, the corresponding gradient magnitude is redefined and a new algorithm for non-maximum suppression is described. The experimental results of edge detection for several test images are provided to demonstrate our approach. [Copyright &y& Elsevier]

Abstract: In this paper we consider a conic trust-region method for unconstrained optimization problems and analyze its convergence properties. We propose a convenient curvilinear search method to approximately solve the arising conic trust-region subproblem. Note that this approximate method preserves the strong convergence properties of the exact solution methods and is easy to implement. Both the linear and superlinear convergence of the method are established under commonly used conditions. Numerical experiments are conducted to show the efficiency of the new method. [Copyright &y& Elsevier]

Abstract: This paper is devoted to construction interpolatory multiscaling functions with a general dilation factor . We first show two-scale matrix symbol associated with interpolatory multiscaling functions is reduced to a special form. Also, a characterization on approximation order for the multiscaling functions is described in terms of elements of this special two-scale matrix symbol. Then, an algorithm is provided for constructing compactly supported interpolating multiscaling functions with dilation factor and higher approximation order. Finally, the associated several families examples with one-parameter or two-parameters are explicitly presented. The optimal parameter values which make multiscaling functions provide the highest regularity are also computed. [Copyright &y& Elsevier]

Abstract: Many learning algorithms use hypothesis spaces which are trained from samples, but little theoretical work has been devoted to the study of these algorithms. In this paper we show that mathematical analysis for these algorithms is essentially different from that for algorithms with hypothesis spaces independent of the sample or depending only on the sample size. The difficulty lies in the lack of a proper characterization of approximation error. To overcome this difficulty, we propose an idea of using a larger function class (not necessarily linear space) containing the union of all possible hypothesis spaces (varying with the sample) to measure the approximation ability of the algorithm. We show how this idea provides error analysis for two particular classes of learning algorithms in kernel methods: learning the kernel via regularization and coefficient based regularization. We demonstrate the power of this approach by its wide applicability. [Copyright &y& Elsevier]

Abstract: In this paper, we formulate two repair-time limit replacement problems with imperfect repair under earning rate criteria with and without discounting. First, the optimal repair-time limits which maximize the long-run average profit rate and the expected total discounted profit over an infinite time horizon are analytically derived. Next, we develop the nonparametric algorithms for estimating the optimal repair-time limits, provided that the complete sample data of repair time are given. The basic idea is to apply the Lorenz statistics and to transform the underlying algebraic problems to the graphical ones. Finally, we present some numerical examples to show that the proposed algorithms can be useful to estimate the profit-based repair limit replacement schedule. [Copyright &y& Elsevier]

Abstract: This paper concentrates on a limited-flow network in which each node and branch has a designated capacity, which will have different lower levels due to various partial and complete failures. We try to evaluate the system unreliability that the maximum flow of the network is less than or equal to the demand d without exceeding the budget B. First, a simple algorithm in terms of minimal cuts is proposed to generate all (d, B)-MCs in order to evaluate the system unreliability. A computer example is shown to illustrate the solution procedure. [Copyright &y& Elsevier]

Abstract: In this paper, we study numerical behavior of several computational variants of the Gram-Schmidt orthogonalization process. We focus on the orthogonality of computed vectors which may be significantly lost in the classical or modified Gram-Schmidt algorithm, while the Gram-Schmidt algorithm with reorthogonalization has been shown to compute vectors which are orthogonal to machine precision level. The implications for practical implementation and its impact on the efficiency in the parallel computer environment are considered. [Copyright &y& Elsevier]

Abstract: One of the main problems dealing with iterative methods for solving polynomial systemsis the initialization of the iteration. This paper provides an algorithm to initialize the search of solutions of polynomial systems. [Copyright &y& Elsevier]

Abstract: We propose a “fast” algorithm for the construction of a data-sparse inverse of a generalToeplitz matrix. The computational cost for inverting an N × N Toeplitz matrix equals the cost of four length-N FFTs plus an O(N)-term. This cost should be compared to the O(N log2 N) cost of previously published methods. Moreover, while those earlier methods are based on algebraic considerations, the procedure of this paper is analysis-based; as a result, its stability does not depend on the symmetry and positive-definiteness of the matrix being inverted. The performance of the scheme is illustrated with numerical examples. [Copyright &y& Elsevier]