NEWTON SCHULZ METHOD FOR SOLVING NONLINEAR MATRIX EQUATION Xp plus A*XA = Q

被引：0

作者：

Kim, Hyun-Min ^{[1
]}

Kim, Young-Jin ^{[2
]}

Meng, Jie ^{[1
]}

机构：

[1] Pusan Natl Univ, Dept Math, Busan 46241, South Korea

[2] Natl Inst Math Sci, Innovat Ctr Ind Math, Gyeonggi Do 13488, South Korea

来源：

JOURNAL OF THE KOREAN MATHEMATICAL SOCIETY | 2018年 / 55卷 / 06期

关键词：

fixed-point iteration; Newton's method; Newton-Schulz algorithm; local convergence; POSITIVE-DEFINITE SOLUTION; PTH; ITERATIONS;

D O I：

10.4134/JKMS.j170809

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

The matrix equation X-p + A*XA = Q has been studied to find the positive definite solution in several researches. In this paper, we consider fixed-point iteration and Newton's method for finding the matrix p-th root. From these two considerations, we will use the Newton-Schulz algorithm (N.S.A). We will show the residual relation and the local convergence of the fixed-point iteration. The local convergence guarantees the convergence of N.S.A. We also show numerical experiments and easily check that the N.S. algorithm reduce the CPU-time significantly.

引用

页码：1529 / 1540

页数：12

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