Search

Abstract: We study a family of orthogonal polynomials which generalizes a sequence of polynomials considered by L. Carlitz. We show that they are a special case of the Sheffer polynomials and point out some interesting connections with certain Sobolev orthogonal polynomials. [Copyright &y& Elsevier]

Abstract: In this paper, we improve the preconditioned AOR method of linear systems considered by Evans et al. [The AOR iterative method for new preconditioned linear systems, Comput. Appl. Math. 132 (2001) 461–466]. In Evans’ paper, the coefficient matrix of linear system have to be an L-matrix with , and . When for some , the preconditioned method is invalid. In order to solve the above problem, a new preconditioner is presented. Meanwhile, some recent results are improved. [Copyright &y& Elsevier]

Abstract: This paper presents the explicit expression for matrix right symmetry factor with prescribed rang and null space. Moreover, the explicit expression for generalized inverse , which is a {2,3}-inverse of having the prescribed rang and null space , is derived. As an application, two numerical examples are given. [Copyright &y& Elsevier]

Abstract: In this paper, a subspace limited memory BFGS algorithm for solving large-scale bound constrained optimization problems is developed. It is modifications of the subspace limited memory quasi-Newton method proposed by Ni and Yuan [Q. Ni, Y.X. Yuan, A subspace limited memory quasi-Newton algorithm for large-scale nonlinear bound constrained optimization, Math. Comput. 66 (1997) 1509–1520]. An important property of our proposed method is that more limited memory BFGS update is used. Under appropriate conditions, the global convergence of the method is established. The implementations of the method on CUTE test problems are presented, which indicate the modifications are beneficial to the performance of the algorithm. [Copyright &y& Elsevier]

Abstract: In this paper we consider constructing some higher-order modifications of Newton’s method for solving nonlinear equations which increase the order of convergence of existing iterative methods by one or two or three units. This construction can be applied to any iteration formula, and per iteration the resulting methods add only one additional function evaluation to increase the order. Some illustrative examples are provided and several numerical results are given to show the performance of the presented methods. [Copyright &y& Elsevier]

Abstract: In this paper, variational iteration method (VIM) is used to obtain numerical and analytical solutions for the Zakharov–Kuznetsov equations with fully nonlinear dispersion. Comparisons with exact solution show that the VIM is a powerful method for the solution of nonlinear equations. [Copyright &y& Elsevier]

Abstract: The aim of this paper is to show how geometric and algebraic approaches lead us to a new symplectic elementary transformations: the 2-D symplectic Householder transformations. Their features are studied in details. Their interesting properties allow us to construct a new algorithm for computing a SR factorization. This algorithm is based only on these 2-D symplectic Householder transformations. Its new features are highlighted. The study shows that, in the symplectic case, the new algorithm is the corresponding one to the classical QR factorization algorithm, via the Householder transformations. Some numerical experiments are given. [Copyright &y& Elsevier]

Abstract: In this paper, using a minimum principle for Schur complements of positive semidefinite Hermitian matrices and some estimates of the eigenvalues and the singular values, we obtain some inequalities for the eigenvalues of the Schur complement of the matrix product in terms of the eigenvalues of the Schur complements of and A. [Copyright &y& Elsevier]

Abstract: In the recent paper of Gan and Huang (Linear Algebra Appl. 374 (2003) 317), several simple criteria, as well as a necessary condition for nonsingular H-matrices, have been obtained. Inspired by this work, we will define several new subclasses of nonsingular H-matrices and give necessary conditions for a matrix to be an H-matrix. Finally, as a result of numerical experiments, we establish relations between defined and some already known subclasses. [Copyright &y& Elsevier]

Abstract: In (simple) Pál-type interpolation the problem consists of finding a polynomial of degree that has prescribed values at, say, n pairwise distinct points and prescribed values for the rth derivative at (another) set of m distinct points. The problem is named regular if it has a unique solution for any set of data; this is equivalent to the homogeneous problem (all prescribed values are 0) having the trivial solution only. In this paper the effect of interchanging the value-nodes and the derivative-nodes on the regularity of the problem is studied for several sets of nodes. [Copyright &y& Elsevier]

Abstract: Starting from the coefficients of the power expansions for the Dawson''s integral both around the origin and infinity, a linear functional acting on the space of Laurent polynomials is defined. In this paper, properties of this functional are studied in connection with certain sequences of orthogonal Laurent polynomials and two-point Padé approximants. [Copyright &y& Elsevier]

Abstract: We establish Mehler–Heine-type formulas for orthogonal polynomials related to rational modifications of Hermite weight on the real line and for Hermite–Sobolev orthogonal polynomials. These formulas give us the asymptotic behaviour of the smallest zeros of the corresponding orthogonal polynomials. Furthermore, we solve a conjecture posed in a previous paper about the asymptotics of the smallest zeros of the Hermite–Sobolev polynomials as well as an open problem concerning the asymptotics of these Sobolev orthogonal polynomials. [Copyright &y& Elsevier]

Abstract: In this paper we consider polynomials orthogonal with respect to an oscillatory weight function on , where is an integer. The existence of such polynomials as well as several of their properties (three-term recurrence relation, differential equation, etc.) are proved. We also consider related quadrature rules and give applications of such quadrature rules to some classes of integrals involving highly oscillatory integrands. [Copyright &y& Elsevier]

Abstract: This paper deals with the classes of strong distribution functions defined on the interval , , where . The classification is such that the distribution function has a (reciprocal) symmetry, depending on , about the point . We consider properties of the L-orthogonal polynomials associated with . Through linear combination of these polynomials we relate them to the L-orthogonal polynomials associated with some . [Copyright &y& Elsevier]

Abstract: For any conforming mesh, the application of a skeleton-regular partition over each element in the mesh, produces a conforming mesh such that all the topological elements of the same dimension are subdivided into the same number of child-elements. Every skeleton-regular partition has associated special constitutive (recurrence) equations. In this paper the average adjacencies associated with the skeleton-regular partitions in 3D are studied. In three-dimensions different values for the asymptotic number of average adjacencies are obtained depending on the considered partition, in contrast with the two-dimensional case [J. Comput. Appl. Math. 140 (2002) 673]. In addition, a priori formulae for the average asymptotic adjacency relations for any skeleton-regular partition in 3D are provided. [Copyright &y& Elsevier]

Abstract: In this paper, we investigate the global behavior of the recursive sequencewhere and is a continuous function defined on , which satisfies some additional conditions. [Copyright &y& Elsevier]

Abstract: This paper is devoted to the study of the stability of the solutions of the first order implicit difference periodic equationWe prove that if there exist a pair of lower and upper solutions respectively of this problem together with a suitable condition on the function and it has at most two solutions in the sector , then one of such solutions is asymptotically stable. Moreover, it is proved the optimality of the given results, both in the conditions imposed on and in the number of the periodic solutions. [Copyright &y& Elsevier]

Systems of algebraic equations with interval coefficients are very common in several areas of engineering sciences. The computation of the solution of such systems is a central problem when the characterization of the variables related by such systems is desired.In this paper we characterize the solution of systems of algebraic equations with real interval coefficients. The characterization is obtained considering the approach introduced in J. Comput. Appl. Math. 136 (2001) 271. [Copyright &y& Elsevier]

Let (λ,x) be an eigenpair of the matrix A of order n and let (μ,u) be a Ritz pair of A with respect to a subspace K. Saad has derived a simple priori error bound for sin∠(x,u) in terms of sin∠(x,K) for A Hermitian. Similar to Saad''s result, Stewart has got an equally simple inequality for A non-Hermitian. In this paper, let (θ,w) be a harmonic Ritz pair from a subspace K, a similar priori error bound for sin∠(x,w) is established in terms of sin∠(x,K). [Copyright &y& Elsevier]

In this paper, several new theorems on the stability of impulsive control systems are presented. These theorems are then used to find the conditions under which the nuclear spin generator can be asymptotically controlled to the equilibrium point by using impulsive control. Given the parameters of the nuclear spin generator and the impulsive control law, we also present a theory of impulsive synchronization of two nuclear spin generators. Moreover, a larger upper bound of impulsive intervals for the stabilization and synchronization can be obtained. [Copyright &y& Elsevier]