Taiwanese Journal of Mathematics

ON POSITIVE DEFINITE SOLUTIONS OF THE MATRIX EQUATION $X+A∗X^{-q}A=Q(0 \lt q ≤ 1)$

Xiaoyan Yin, Sanyang Liu, and Tiexiang Li

Full-text: Open access

Abstract

Consider the nonlinear matrix equation $X+A^{*}X^{-q}A = Q$ where $0 \lt q \leq 1$. A new sufficient condition for this equation to have positive definite solution is provided and two iterative methods for the maximal positive definite solution are proposed. Applying the theory of condition number developed by Rice, an explicit expression of the condition number of the maximal positive definite solution is obtained. The theoretical results are illustrated by numerical examples.

Article information

Source
Taiwanese J. Math., Volume 16, Number 4 (2012), 1391-1407.

Dates
First available in Project Euclid: 18 July 2017

Permanent link to this document
https://projecteuclid.org/euclid.twjm/1500406740

Digital Object Identifier
doi:10.11650/twjm/1500406740

Mathematical Reviews number (MathSciNet)
MR2951144

Subjects
Primary: 15A24: Matrix equations and identities 65F10: Iterative methods for linear systems [See also 65N22] 65H05: Single equations

Keywords
nonlinear matrix equation positive definite solution condition number

Citation

Yin, Xiaoyan; Liu, Sanyang; Li, Tiexiang. ON POSITIVE DEFINITE SOLUTIONS OF THE MATRIX EQUATION $X+A∗X^{-q}A=Q(0 \lt q ≤ 1)$. Taiwanese J. Math. 16 (2012), no. 4, 1391--1407. doi:10.11650/twjm/1500406740. https://projecteuclid.org/euclid.twjm/1500406740


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