๐”– Bobbio Scriptorium
โœฆ   LIBER   โœฆ

Symmetric multisplitting of a symmetric positive definite matrix

โœ Scribed by Zhi-Hao Cao; Zhong-Yun Liu

Publisher
Elsevier Science
Year
1998
Tongue
English
Weight
562 KB
Volume
285
Category
Article
ISSN
0024-3795

No coin nor oath required. For personal study only.

โœฆ Synopsis

A parallel symmetric multisplitting method for solving a symmetric positive system Ax = b is presented. Here the s.p.d. (symmetric positive definite) matrix A need not be assumed in a special form (e.g. the dissection form (R.E. White, SIAM J. Matrix Anal. Appl. 11 (1990) 69-82). The main tool for deriving our method is the diagonally compensated reduction (cf. (0. Axelsson, L. Kolotilina, Numer. Linear Algebra Appl. 1 (1994) 155-177)). The convergence of the presented parallel symmetric multisplitting method is also discussed by using this tool.

๐Ÿ“œ SIMILAR VOLUMES

Nonstationary two-stage multisplitting m
Nonstationary two-stage multisplitting methods for symmetric positive definite matrices
โœ Zhong-Yun Liu; Lu Lin; Chun-Chao Shi ๐Ÿ“‚ Article ๐Ÿ“… 2000 ๐Ÿ› Elsevier Science ๐ŸŒ English โš– 506 KB

Nonstationary synchronous two-stage multisplitting methods for the solution of the symmetric positive definite linear system of equations are considered. The convergence properties of these methods are studied. Relaxed variants are also discussed. The main tool for the construction of the two-stage

Approximating the inverse of a symmetric
Approximating the inverse of a symmetric positive definite matrix
โœ Gordon Simons; Yi-Ching Yao ๐Ÿ“‚ Article ๐Ÿ“… 1998 ๐Ÿ› Elsevier Science ๐ŸŒ English โš– 405 KB

It is shown for an n x n symmetric positive definite matrix T = (t, j) with negative offdiagonal elements, positive row sums and satisfying certain bounding conditions that its inverse is well approximated, unifornaly to order l/n 2, by a matrix S = (s,,,