关于不可约弱广义对角优势阵

本讨论了不可约弱广义对角优势阵的非奇异性及其特征值的分布,进而给出了非奇异Ｍ－阵的几个充分条件。     

一类广义对角占优矩阵

对角占优型矩阵的研究一直是诸多领域中广泛关注的问题．本文讨论了一类广义对角占优矩阵,得到了其优良性质,以及与重要矩阵类拟对角占优矩阵和Ｍ矩阵的关系     

On orthogonal polynomials with respect to the form -(x - c)S'

Summary A form (linear functional) $u$ is called regular if we can associate with it a sequence of monic orthogonal polynomials. On certain regularity conditions, the product of a non regular form by a polynomial can be regular. The purpose of this work is to establish regularity conditions of the form $-(x-c){\mathbf S}',$ where ${\mathbf S}$ is a classical (Bessel, Jacobi). We give the second-order recurrence relations and structure relations of its corresponding orthogonal polynomial sequence. We conclude with an example as an illustration.     

A note on a conjecture about cycles with many incident chords

Given positive integers n and k, let g_k(n) denote the maximum number of edges of a graph on n vertices that does not contain a cycle with k chords incident to a vertex on the cycle. Bollobás conjectured as an exercise in [2, p. 398, Problem 13] that there exists a function n(k) such that g_k(n) = (k + 1)n ? (k + 1)² for all n ≥ n(k). Using an old result of Bondy [ 3 ], we prove the conjecture, showing that n(k) ≤ 3 k + 3. © 2004 Wiley Periodicals, Inc. J Graph Theory 46: 180–182, 2004     

非奇异H矩阵的实用充分条件

In this paper, several practical sufficient conditions for nonsinguular H-matrices are obtained by comparing the elements of a matrix. Advantage of results obtained is illustrated by a numerical example.     

High performance solution of partial differential equations discretized using a Chebyshev spectral collocation method

When a Chebyshev spectral collocation method is applied to a flow problem in a rectangularly decomposable domain it leads to the solution of a structured linear system. Since the linear system is solved at each step of a Newton-type iterative process an efficient method to solve it needs to be provided. A level 3 BLAS-based algorithm is presented and its efficiency is studied.     

DIAGONAL REDUCTION OVER sπr IDEALS

This article introduces a new class of ideals, namely, the sπr ideals. It is shown that every regular square matrix over sπr ideals of a ring admits a diagonal reduction.     

对角因子循环矩阵Moore-Penrose逆及奇异值分解

给出了对角因子循环矩阵的Mooore—Penrose逆的表达式，并利用得到的表达式可以给出Moore—Penrose逆的快速算法．进一步研究了实对角因子循环矩阵的奇异值分解，并利用Hartley变换矩阵，给出了奇异值分解的具体表达式．     

On the Square Root of an H-matrix with Positive Diagonal Elements

This paper proves that for an H-matrix with positive diagonal elements there exists one and only one square root which is also an H-matrix with positive diagonal elements. An algorithm approaching the square root is proposed.     

A method for finite element parallel viscous compressible flow calculations

This paper presents the parallelization aspects of a solution method for the fully coupled 3D compressible Navier-Stokes equations. The algorithmic thrust of the approach, embedded in a finite element code NS3D, is the linearization of the governing equations through Newton methods, followed by a fully coupled solution of velocities and pressure at each non-linear iteration by preconditioned conjugate gradient-like iterative algorithms. For the matrix assembly, as well as for the linear equation solver, efficient coarse-grain parallel schemes have been developed for shared memory machines, as well as for networks of workstations, with a moderate number of processors. The parallel iterative schemes, in particular, circumvent some of the difficulties associated with domain decomposition methods, such as geometry bookkeeping and the sometimes drastic convergence slow-down of partitioned non-linear problems.