Geometrical Inverse Preconditioning for Symmetric Positive Definite Matrices

被引：2

作者：

Chehab, Jean-Paul ^{[1
]}

Raydan, Marcos ^{[2
]}

机构：

[1] Univ Picardie Jules Verne, LAMFA, CNRS, UMR 7352, 33 Rue St Leu, F-80039 Amiens, France

[2] Univ Simon Bolivar, Dept Comp Cient & Estadist, Ap 89000, Caracas 1080A, Venezuela

来源：

MATHEMATICS | 2016年 / 4卷 / 03期

关键词：

preconditioning; cones of matrices; gradient method; minimal residual method; APPROXIMATE-INVERSE; ITERATIVE METHOD; EQUATIONS;

D O I：

10.3390/math4030046

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We focus on inverse preconditioners based on minimizing F (X) = 1 - cos (XA, I), where XA is the preconditioned matrix and A is symmetric and positive definite. We present and analyze gradient-type methods to minimize F (X) on a suitable compact set. For this, we use the geometrical properties of the non-polyhedral cone of symmetric and positive definite matrices, and also the special properties of F (X) on the feasible set. Preliminary and encouraging numerical results are also presented in which dense and sparse approximations are included.

引用

页数：20

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