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In this paper we first write a proof of the perceptron convergence algorithm for the complex multivalued neural networks (CMVNNs). Our primary goal is to formulate and prove the perceptron convergence algorithm for the bicomplex multivalued neural networks (BMVNNs) and other important results in the theory of neural networks based on a bicomplex algebra. [ABSTRACT FROM AUTHOR]

Abstract: Probably the popular form of binary genetic algorithms for function optimization use tournament selection (TS) or roulette wheel selection (RS) for function optimization. Also single point crossover (SC) and uniform crossover (UC) are most popular and effective crossover operators. In an earlier paper we had considered all four combinations of these crossover and mutation operators along with bit-wise mutation, called GA1 (TS+SC), GA2 (TS+UC), GA3 (RS+SC) and GA4 (RS+UC). In this paper, an attempt is made to hybridize these four GAs by incorporating the quadratic approximation (QA) operator into them. The four resultant hybrid GAs, called HGA1, HGA2, HGA3 and HGA4, are compared with the four simple GAs on a set of 22 test problems taken from literature. Based on the extensive numerical and graphical analysis of results it is concluded that the HGA3 outperforms all rest 7 versions. Further, we study the depth and frequency of the QA should be applied for better performance for the particular problem suite. [Copyright &y& Elsevier]

Abstract: This paper presents a survey of error-free algorithms to solve various systems of linear equations. The presented algorithms do not introduce computational errors into the solution and thus they are well suited to solve ill-conditioned linear systems. The error-free algorithms are based on modulo arithmetic. Two basic approaches have been investigated in the paper. The first one is based on iterative scheme using one modulus only. The other one is parallel and uses several moduli and the Chinese theorem. It is based on polynomial algebra operations that allow to express the operation of deconvolution as a sequence of convolutions of both response and output signals. [Copyright &y& Elsevier]

Abstract: In this paper, we formulate a new robust two-species nonautonomous predator–prey model with multi-delays and impulsive effects and perform a systematic mathematical and ecological study. Our results in this paper indicate that under the appropriate linear periodic impulsive perturbations, the system is permanent and has a unique positive globally attractive semi-trivial periodic solution. By using the Brouwer fixed point theorem, we prove that if the periodic system is permanent, then there is at least one positive periodic solution of the system. We show that the conditions for global attractivity of the positive semi-trivial periodic solution and permanence of the population of the model depend on time delay, so, we call it “profitless”. In this paper, the main feature is that we introduce multi-delays and impulses into the predator–prey model, exhibit a new modeling method which is applied to investigate multi-species impulsive multi-delays differential equations. [Copyright &y& Elsevier]

Abstract: A detailed, comparative study of the numerical stability of the recursive algorithms, widely used to calculate the Zernike moments of an image, is presented in this paper. While many papers, introducing fast algorithms for the computation of Zernike moments have been presented in the literature, there is not any work studying the numerical behaviour of these methods. These algorithms have been in the past compared to each other only according to their computational complexity, without been given the appropriate attention, as far as their numerical stability is concerned, being the most significant part of the algorithms’ reliability. The present contribution attempts to fill this gap in the literature, since it mainly demonstrates that the usefulness of a recursive algorithm is defined not only by its low computational complexity, but most of all by its numerical robustness. This paper exhaustively compares some well known recursive algorithms for the computation of Zernike moments and sets the appropriate conditions in which each algorithm may fall in an unstable state. The experiments show that any of these algorithms can be unstable under some conditions and thus the need to develop more stable algorithms is of major importance. [Copyright &y& Elsevier]

Abstract: This paper develops an Improved harmony search (IHS) algorithm for solving optimization problems. IHS employs a novel method for generating new solution vectors that enhances accuracy and convergence rate of harmony search (HS) algorithm. In this paper the impacts of constant parameters on harmony search algorithm are discussed and a strategy for tuning these parameters is presented. The IHS algorithm has been successfully applied to various benchmarking and standard engineering optimization problems. Numerical results reveal that the proposed algorithm can find better solutions when compared to HS and other heuristic or deterministic methods and is a powerful search algorithm for various engineering optimization problems. [Copyright &y& Elsevier]

Abstract: Network managers wish to optimize control parameters such as signal setting which are very related to the traffic assignment models. On the other hand traffic assignment patterns as an important instrument for predicting the amount of flow on network links are dependent to control decisions. According to the significance of this concept, some important papers about this mutually relation are reviewed in this paper. Then we implement a nonlinear algorithm on a minimal cost multicommodity flow (MCMF) problem to optimize some control policies subject to optimal flows. Although we take signal times into account, but this approach has a far more reaching application in urban network control and design. We employ a hybrid intelligent algorithm integrating decent direction algorithm and an interior point algorithm in a mutually consistent scheme for obtaining optimal signals and equilibrium flows. An example is given to illustrate the effectiveness of our scheme. [Copyright &y& Elsevier]

Abstract: This paper presents an outcome-space finite algorithm for solving linear multiplicative programming, in each iteration of which a convex quadratic programming is only solved. In the paper, we give a global optimization condition on a class of multiplicative programming problems and prove that the proposed algorithm is finite terminative and gain a global optimal solution of the former problem when it stops. It can be shown by the numerical results that the proposed algorithm is effective and the computational results can be gained in short time. [Copyright &y& Elsevier]

Abstract: In this paper, we extend technique for order preference by similarity ideal solution (TOPSIS) for solving large scale multiple objective programming problems involving fuzzy parameters. These fuzzy parameters are characterized as fuzzy numbers. For such problems, the α-Pareto optimality is introduced by extending the ordinary Pareto optimality on the basis of the α-level sets of fuzzy numbers. An interactive fuzzy decision making algorithm for generating α-Pareto optimal solution through TOPSIS approach is provided where the decision maker (DM) is asked to specify the degree α and the relative importance of objectives. Finally, a numerical example is given to clarify the main results developed in the paper. [Copyright &y& Elsevier]

In this paper, by using the theories and methods of mathematical analysis and computer algebra, a new algorithm of symbolic integral was established, a new Maple procedure myint for it was established, too. And it was applied to the automatic proving the mean-value theorems for derivatives. The results indicated that the algorithm of symbolic integral had been established in this paper had advantage of simple idea, excellent property for operation and powerful competence. This would be useful for the problem of solving differential equations, automatic proving some mathematical theorems, and so on. [Copyright &y& Elsevier]

• In this paper, we proposed an algorithm to solve mixed solutions of the matrix Equation ∑ i = 1 t A i X i B i = E with sub-matrix constraints. We also prove that the iterative solution sequence generated by the algorithm is convergent. Moreover, for a given matrix, its best approximation is obtained, which is the mixed solution of the matrix equation with sub-matrix constraints. Finally, a large number of numerical experiments are carried out, and results show that the algorithm is effective not only in image restoration, but also in the general case, for both small-scale and large-scale matrices. The work belongs to the field of numerical algebra, and has been widely concerned. We put forward and analyze in details an iterative method to find the mixed solutions of a matrix equation with sub-matrix constraints. The convergence of the approximated solution sequence generated by the iterative method is investigated, showing that if the constrained matrix equation is consistent, the mixed solution group can be obtained after a finite number of iterations. Moreover, for a given matrix, its best approximation is obtained, which is the mixed solution of the matrix equation with sub-matrix constraints. Finally, a large number of numerical experiments are carried out, and results show that the algorithm is effective not only in image restoration, but also in the general case for both small-scale and large-scale matrices. [ABSTRACT FROM AUTHOR]

Abstract: In this paper we apply the idea of Dixon resultant to algebraic differential equations and introduce the Dixon differential resultant. We prove that a necessary condition for the existence of a common solution of two algebraic differential equations is that the differential resultant is equal to zero, which actually provides a method of elimination and reduces a system of multi-variate differential equations to a system of single-variate differential equations. This result is also generalized to the system of n differential polynomials. We give algorithms to realize our method of elimination for systems of differential equations. Our results and algorithms are demonstrated by some examples. [Copyright &y& Elsevier]

Abstract: The C-Algorithm introduced in is designed to determine isochronous centers for Lienard-type differential systems, in the general real analytic case. However, it has a large complexity that prevents computations, even in the quartic polynomial case. The main result of this paper is an efficient algorithmic implementation of C-Algorithm, called ReCA (Reduced C-Algorithm). Moreover, an adapted version of it is proposed in the rational case. It is called RCA (Rational C-Algorithm) and is widely used in to find many new examples of isochronous centers for the Liénard type equation. [Copyright &y& Elsevier]

Abstract: In this paper, integrodifferential systems are converted into a system of algebraic equations by hybrid of general block-pulse functions and the second Chebyshev polynomials. The approximate solutions of integrodifferential systems are derived. The numerical examples illustrate that the algorithm is valid. [Copyright &y& Elsevier]

Abstract: In this paper, a simple dogleg algorithm for solving new conic model subproblems is proposed, and a quasi-Newton method based on the simple dogleg algorithm is developed. Then the global convergence of the method under some reasonable conditions is established. Numerical experiment shows that this method may be superior to the corresponding method with a quadratic model. [Copyright &y& Elsevier]

Abstract: In this paper we propose parallel algorithm for the solution of partial differential equations over a rectangular domain using the Crank–Nicholson method by cooperation with the DuFort–Frankel method and apply it on a model problem, namely, the heat conduction equation. One of the well known parallel techniques in solving partial differential equations in cluster computing environment is the domain decomposition technique. Using this technique, the whole domain is decomposed into subdomains, each of them has its own boundaries that are called the interface points. Parallelization is realized by approximating interface values using the unconditionally stable DuFort–Frankel explicit scheme, and these values serve as Neumann boundary conditions for the Crank–Nicholson implicit scheme in the subdomains. The numerical results show that our algorithm is more accurate than the algorithm based on the forward explicit method to approximate the values of the interface points, especially, when we use a small number of time steps. Moreover, these numerical results show that increasing the number of processors which are used in the cluster, yields an increase in the algorithm speedup. [Copyright &y& Elsevier]

Abstract: In nonlinear programming problems (especially nonconvex problems), attaining the global optimum is crucial. To reach this purpose, the current paper represents a new genetic algorithm for solving nonconvex nonlinear programming problems. The new method is simpler and more intuitive than the existing models and finds the global optimum of the problem in a reasonable time. The proposed technique, to attain the global optimum of problem (especially in large scale problems) instead of increasing the size of population which usually conduces to the curse of dimensionality – that is widespread in usual genetic algorithms – decomposes the main problem into several sub problems, but with lower size of population in each sub problem. This decomposition has been formed in such a way that it could envelop the total solution space. The proposed genetic algorithm, which determines the sufficient sub problems, could converge to global optimum of problem. To be able to measure the proposed genetic algorithm, several problems have been solved in different spectrums. Herein, it has been shown that the proposed technique, both in run time and in solution quality, is preferred to the usual genetic algorithm in this domain (nonlinear continuous programming problems). [Copyright &y& Elsevier]

Abstract: For a multi-tiered logistics network containing the manufacturers, distributors and consumers, in this paper we present a fast polynomial time algorithm to find product flow with the minimum congestion by shipping products from manufacturers to distributors and from distributors to consumers. Global convergence is delivered for the proposed algorithm. The values of congestion and the potential function can be successfully decreased by conducting the proposed algorithm in logistics networks. Numerical computations and comparisons with well-known linear programming package CPLEX on large-scale logistics networks are performed where significant savings in computations are gained from the proposed algorithm. [Copyright &y& Elsevier]

Abstract: In this paper, we study on Fibonacci search method with k-Lucas numbers by introducing a parameter α which depends on the length of the interval and the function. This parameter ensures that the result we got at the end of the computation is correct. We made more improvement in algorithm which finds the maximum point of a unimodal function. Application of this algorithm gives better results. [Copyright &y& Elsevier]

Abstract: This paper discusses the infinite horizon stochastic Nash games with state-dependent noise. After establishing the asymptotic structure along with the positive semidefiniteness for the solutions of the cross-coupled stochastic algebraic Riccati equations (CSAREs), a new algorithm that combines Newton’s method with two fixed point algorithms for solving the CSAREs is derived. As a result, it is shown that the proposed algorithm attains quadratic convergence and the reduced-order computations for sufficiently small parameter ε. As another important feature, the high-order approximate strategy that is based on the iterative solutions is proposed. Using such strategy, the degradation of the cost functional is investigated. Finally, in order to demonstrate the efficiency of the proposed algorithms, computational examples are provided. [Copyright &y& Elsevier]

Abstract: The haplotype reconstruction based on aligned single nucleotide polymorphism (SNP) fragments is to conclude a pair of haplotypes from located polymorphism data. Known computational model of this problem is minimum error correction (MEC) that has been proved to be NP-complete by Lippert et al., but there are few practical algorithms for it. In this paper, we design a heuristic algorithm based on particle swarm optimization (PSO) which was proposed by Kennedy and Eberhart to solve the problem. Extensive computational experiments indicate that the designed PSO algorithm achieves a higher accuracy than the genetic algorithm (GA) designed by Ruisheng Wang to the MEC model in most cases. [Copyright &y& Elsevier]

Abstract: A new technique for calculating the one-dimensional differential transform of nonlinear functions is developed in this paper. This new technique avoids the difficulties and massive computational work that usually arise from the standard method. The algorithm will be illustrated by studying suitable forms of nonlinearity. Several nonlinear ordinary differential equations, including Troesch’s and Bratu-type problems, are then solved to demonstrate the reliability and efficiency of the proposed scheme. The present algorithm offers a computationally easier approach to compute the transformed function for all forms of nonlinearity. This gives the technique much wider applicability. [Copyright &y& Elsevier]

Abstract: In this paper we propose an affine scaling interior algorithm via Lanczos path for solving nonlinear equality systems subject to bounds on variables. Employing the affine scaling Lanczos path search strategy, we obtain an iterative direction by solving the linearize model. By using the line search backtracking technique, we will find an acceptable trial step length along this direction which is strictly feasible and makes the objective function nonmonotonically decreasing. The global convergence and fast local convergence rate of the proposed algorithm are established under some reasonable conditions. Furthermore, the numerical results of the proposed algorithm indicate to be effective. [Copyright &y& Elsevier]

Abstract: Fractal dimension is a suitable tool for analyzing the nonlinear behaviour and state of the dynamical systems. The algorithms of fractal dimension methods have weak ability to the estimation of complexity in the irregular graphs. In this paper we propose a new algorithm based on the size measure relationship (SMR) method, quantifying the dimensional behaviour of irregular rectifiable graphs with minimum time complexity. The evidence for the suitability (equality with the nature of dimension) of the algorithm is presented. [Copyright &y& Elsevier]

Abstract: The present paper argues that it suffices for an algorithmic time complexity measure to be system invariant rather than system independent (which means predicting from the desk). [Copyright &y& Elsevier]

Abstract: The present paper makes use of factorial experiments to assess software complexity using insertion sort as an example. A new modeling for insertion sort is proposed. It might be of interest to implement the methodology in quicksort and other advanced algorithms. [Copyright &y& Elsevier]

Abstract: In this paper we present the construction of a non-standard explicit algorithm for initial-value problems. The method results to be of second order and A-stable. This new algorithm has been proven to be suitable for solving different kind of initial-value problems, specifically, non-singular problems, singular problems, stiff problems and singularly perturbed problems. Some numerical experiments are considered in order to check the behaviour of the method when applied to a variety of initial-value problems. [Copyright &y& Elsevier]

Abstract: The aim of this paper is to find an accurate and efficient algorithm for evaluating the summation of large sets of floating-point numbers. We present a new representation of the floating-point number system in which a number is represented as a linear combination of integers and the coefficients are powers of the base of the floating-point system. The approach allows to build up an accurate floating-point summation algorithm based on the fact that no rounding error occurs whenever two integer numbers are summed or a floating-point number is multiplied by powers of the base of the floating-point system. The proposed algorithm seems to be competitive in terms of computational effort and, under some assumptions, the computed sum is greatly accurate. With such assumptions, less-conservative in the practical applications, we prove that the relative error of the computed sum is bounded by the unit roundoff. [Copyright &y& Elsevier]

Abstract: In order to speed up long integer modular multiplication and modular exponentiation computations that play the most important role of implementing public-key cryptographic systems, recently a result has been reported by developing a binary complement based approach on operands with larger Hamming weight in their binary representations. It is claimed that this new proposal achieves extremely good performance improvement due to the possible extensive Hamming weight reduction. Furthermore, in the conclusion of this recent result, it is claimed that the larger the bit length of the operands is, the better the performance will be in their algorithms. However, in this paper it will be shown precisely that the considered binary complement based approach on operands can only lead to an extremely negligible Hamming weight reduction. Detailed and exact analysis result is contrary to their claim, i.e., performance improvement of the binary complement based algorithms decreases considerably for larger bit length of the operands. [Copyright &y& Elsevier]

Abstract: In this paper, we investigate numerically positive solutions of the equation −Δu = λf(x, u)+ μg(x, u) with Dirichlet boundary condition in a bounded domain Ω for λ >0, μ ∈ R using sub-super solution algorithm and mountain pass algorithm. We will show that in which range of λ, this problem achieves numerical solutions. [Copyright &y& Elsevier]

Abstract: In this paper we proposed a model for motion detection in video. The model gives a motion map which is combined with other feature maps to create a saliency map. An attention process was implemented on a computer using this algorithm and the results show that it properly reflects a human observer’s attention process to videos. [Copyright &y& Elsevier]

Abstract: This paper presents an alternative computational algorithm for finding the root mean square (RMS) curvature as a nonlinearity measure of nonlinear regression model (NLR model) with two parameters. Specially, the suggested algorithm is applied on a NLR model in which there is a conditionally linear parameter. The algorithm is mainly based on the work presented in [ D.M. Bates, D.G. Watts, Relative curvature measures of nonlinearity (with discussion), Journal of the Royal Statistical Society 42 (1) (1980) 1– 25]. The algorithm is suited for implementation using computer algebra systems (CAS) such as MAPLE, MATLAB, MACSYMA and MATHEMATICA. The researchers compare the results with the corresponding output of the S-PLUS Program for the same considering example and the results in some earlier works. [Copyright &y& Elsevier]

Abstract: In this paper, we investigate the effects of partially integrated production and marketing policy (PIPM) of a manufacturing firm which produces single item with a finite rate. The demand of that item is dependent on its selling price, marketing cost and quality. However, the selling price is determined by a mark-up (prescribed) over the unit production cost dependent on the several factors of the manufacturing system. Incorporating the effects and the possibilities of defective units in the production process, the model is developed by formulating constrained maximization problem of marketing department and minimization problem of production department. Problems are solved by Generalised Reduced Gradient (GRG) method and simple Genetic Algorithm (SGA). Finally, to illustrate the results, a numerical example is given and the results for different methods are compared with each other. [Copyright &y& Elsevier]

Abstract: This paper focuses on two drawbacks on Chang–Lai’s modular square algorithm, the version of the modular square algorithm that uses the generalized Chinese remainder theorem to improve the parallel computational efficiency. According to our results, Chang–Lai’s algorithm is impractical from the application view. [Copyright &y& Elsevier]

Abstract: In this paper, we present a new convergence rate for both symmetric and nonsymmetric positive definite problems. In our theory, “regularity and approximation” assumption is used. A new rate of convergence estimate with is used where α is a “regularity and approximation” parameter. Also, a new convergence rate is given by two-grid schemes. [Copyright &y& Elsevier]

Abstract: The price control problem is an important linear bilevel programming problem. In this paper, we are concerned with a class of weak price control problems with non-unique lower level solutions. For such problems, we study the existence of solution via a penalty method. Then, we propose a simple algorithm for this problem, and present the convergence of the algorithm. The example illustrates that the method is feasible and efficient. [Copyright &y& Elsevier]

Abstract: In this paper, a modified SQP method is presented. The algorithm starts from an arbitrary initial point and can overcome the Maratos effect. Moreover, it avoid choosing the penalty parameters. Under some reasonable conditions, the global convergence is shown. [Copyright &y& Elsevier]

Abstract: In this paper, we consider a deterministic global optimization algorithm for solving a general linear sum of ratios (LFP). First, an equivalent optimization problem (LFP1) of LFP is derived by exploiting the characteristics of the constraints of LFP. By a new linearizing method the linearization relaxation function of the objective function of LFP1 is derived, then the linear relaxation programming (RLP) of LFP1 is constructed and the proposed branch and bound algorithm is convergent to the global minimum through the successive refinement of the linear relaxation of the feasible region of the objection function and the solutions of a series of RLP. And finally the numerical experiments are given to illustrate the feasibility of the proposed algorithm. [Copyright &y& Elsevier]

Abstract: On a network with nonnegative-length edges, Dijkstra’s shortest path algorithm computes single-source shortest path in O(m + n log n) time. The time bound assumes that a Fibonacci heap is used during the implementation of Dijkstra’s algorithm. As the process of building heaps needs a little complex work, it makes the algorithm not easy to be used. In this paper, we make some very simple, but useful, changes in the original Dijkstra algorithm and obtain a new improved Dijkstra’s shortest path algorithm that avoids the process of building heap and runs in O(m + D max log(n!)) time. Here m, n and D max are the number of edges, vertices and the maximal number of edges incident with vertex, respectively. Thus, the new algorithm is very competitive for those sparse networks especially in road traffic networks in which D max is often a small number. [Copyright &y& Elsevier]

Abstract: We developed an algorithm in Kıymaz and Mirasyedioğlu [O. Kıymaz and Ş. Mirasyedioğlu, An algorithmic approach to exact power series solutions of second order linear homogeneous differential equations with polynomial coefficients, Appl. Math. Comp. 139 (1) (2003) 165–178] for computing exact power series solutions of second order linear homogeneous differential equations with polynomial coefficients, near a point x = x 0. In this paper we present a symbolic algorithm to compute the exact power series solutions of nth order linear homogeneous differential equations with polynomial coefficients, near an ordinary point. [Copyright &y& Elsevier]

Abstract: In this paper, a bilevel time minimizing assignment problem is studied in which the aim is to find an optimal partition of the set of n facilities into two mutually disjoint subsets L 1 and L 2 where, L 1 contains m facilities called Level-I facilities and L 2 contains the remaining (n − m) facilities termed as Level-II facilities. The partition is to be optimal in the sense that for this partition the sum of the completion times of the jobs assigned to Level-I and Level-II facilities is the least. It is assumed that all the jobs are to be done, each facility works only on one job, and on each job only one facility works. Further Level-II facilities start working simultaneously on their respective assigned jobs only after Level-I facilities, working in parallel, have finished their jobs. For a feasible assignment denotes the completion time of the jobs assigned to Level-I facilities and that of the jobs assigned to Level-II facilities. Depending on m is greater or smaller than (n − m), the pairs of the type and of the completion times of the jobs assigned to Level-I and Level-II facilities are generated and an optimal partition of the set of n facilities is determined corresponding to the pair for which is the least. To obtain the global minimizer of the proposed problem, a polynomial time algorithm is presented which has been coded in C++ and an empirical analysis has been carried out with the help of randomly generated test problems. [Copyright &y& Elsevier]

Abstract: In this paper, based on the Hirota bilinear method, a reliable algorithm for generating bilinear form of a class of nonlinear partial differential equations (NPDE) is described and a Maple package Bilinearization is established. The package will be helpful for looking for the bilinear form of NPDE by logarithm transformation. [Copyright &y& Elsevier]

Abstract: This paper presents a branch-and-bound algorithm for globally solving a wide class of generalized linear fractional programming problems (GLFP). This class includes such problems as: minimizing a sum, or error for product of a finite number of ratios of linear functions, linear multiplicative programming, polynomial programming, etc. – over nonconvex feasible region. First a problem (Q) is derived which is equivalent to problem (GLFP). In the algorithm, lower bounds are derived by solving a sequence of linear relaxation programming problems, which is based on the construction of the linear lower bounding functions for the objective function and constraint functions of problem (Q) over the feasible region. Convergent property of the presented algorithm is proved and numerical results are given to show the feasibility of the proposed algorithm. [Copyright &y& Elsevier]

Abstract: In this paper we give an algorithm for finding the coefficients in the three term recurrence relation for the polynomials orthogonal with respect to the weight function W(x)=∣x − b∣2α exp[−(x + c)2] on , where , 2α >−1. The algorithm is based on the discretization technique proposed by Gautschi, with the Lanczos algorithm. Using the coefficients obtained by this algorithm we construct the Gauss quadrature rules relative to the weight function W(x). To show the performance of the new algorithm we give some numerical examples. [Copyright &y& Elsevier]

Abstract: In this paper we present some notes of the PageRank algorithm, including its L 1 condition number and some observation of the numerical tests of two variant algorithms which are based on the extrapolation method. [Copyright &y& Elsevier]

Abstract: This paper describes multigrid algorithms for solving multigroup neutron transport equations. Local mode analysis of multilevel is performed for transport problems, and numerical Fourier analysis is carried out to study the smoothing and convergence properties of the multigrid algorithms for neutron diffusion and general P N approximate case respectively. Numerical test calculations validate the theoretical predictions. [Copyright &y& Elsevier]

Abstract: In this paper, we propose two new algorithms based on modified global Arnoldi algorithm for solving large Sylvester matrix equations AX + XB = C where , , X and . These algorithms are based on the global FOM and GMRES algorithms and we call them by Global FOM-Sylvester-Like (GFSL) and Global GMRES-Sylvester-Like (GGSL) algorithms, respectively. Some theoretical results and numerical examples are also given. [Copyright &y& Elsevier]

Abstract: In this paper, by using the theories and methods of mathematics analysis, ordinary differential equation and computer algebra, a reliable algorithm for solving ordinary differential equation (ODE) was established, and a new Maple procedure mechodeproc was established, too. The results of the examples indicated that the procedure mechodeproc based on Taylor polynomial method was simple and effective, and could provide an accuracy approximate solution or exact solution of the ordinary differential equation. This would be useful for solving differential equation. [Copyright &y& Elsevier]

Abstract: In this paper we introduce a reliable symbolic implementation of the algorithm for calculating Adomian polynomials and present some examples to show the simplicity and efficiency of the new method. [Copyright &y& Elsevier]

Abstract: In this paper, by using theories of stochastic process and computer algebra, a reliable algorithm for computing the high-order transition probability matrix of finite Markov chain is established, a new mechanical procedure markovproc is established, too. The procedure markovproc give not only the exact expression of the Markov chains, but also the limiting probability. Some examples are presented to illustrate the implementation of the algorithm. [Copyright &y& Elsevier]