Computing the extremal positive definite solutions of a matrix equation

Xingzhi Zhan

doi:10.1137/S1064827594277041

Computing the extremal positive definite solutions of a matrix equation

Xingzhi Zhan^*

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

137 Scopus citations

Abstract

An efficient and numerically stable implementation of a known algorithm is suggested for finding the extremal positive definite solutions of the matrix equation X + A*X^-1A = I, if such solutions exist. The convergence rate is analyzed. A new algorithm that avoids matrix inversion is presented. Numerical examples are given to illutrate the effectiveness of the algorithms.

Original language	English
Pages (from-to)	1167-1174
Number of pages	8
Journal	SIAM Journal on Scientific Computing
Volume	17
Issue number	5
DOIs	https://doi.org/10.1137/S1064827594277041
State	Published - Sep 1996
Externally published	Yes

Keywords

Iteration
Matrix equation
Positive definite solution

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10.1137/S1064827594277041

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title = "Computing the extremal positive definite solutions of a matrix equation",

abstract = "An efficient and numerically stable implementation of a known algorithm is suggested for finding the extremal positive definite solutions of the matrix equation X + A*X-1A = I, if such solutions exist. The convergence rate is analyzed. A new algorithm that avoids matrix inversion is presented. Numerical examples are given to illutrate the effectiveness of the algorithms.",

keywords = "Iteration, Matrix equation, Positive definite solution",

author = "Xingzhi Zhan",

year = "1996",

month = sep,

doi = "10.1137/S1064827594277041",

language = "英语",

volume = "17",

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T1 - Computing the extremal positive definite solutions of a matrix equation

AU - Zhan, Xingzhi

PY - 1996/9

Y1 - 1996/9

N2 - An efficient and numerically stable implementation of a known algorithm is suggested for finding the extremal positive definite solutions of the matrix equation X + A*X-1A = I, if such solutions exist. The convergence rate is analyzed. A new algorithm that avoids matrix inversion is presented. Numerical examples are given to illutrate the effectiveness of the algorithms.

AB - An efficient and numerically stable implementation of a known algorithm is suggested for finding the extremal positive definite solutions of the matrix equation X + A*X-1A = I, if such solutions exist. The convergence rate is analyzed. A new algorithm that avoids matrix inversion is presented. Numerical examples are given to illutrate the effectiveness of the algorithms.

KW - Iteration

KW - Matrix equation

KW - Positive definite solution

UR - https://www.scopus.com/pages/publications/0000593006

U2 - 10.1137/S1064827594277041

DO - 10.1137/S1064827594277041

M3 - 文章

AN - SCOPUS:0000593006

SN - 1064-8275

VL - 17

SP - 1167

EP - 1174

JO - SIAM Journal on Scientific Computing

JF - SIAM Journal on Scientific Computing

IS - 5

ER -

Computing the extremal positive definite solutions of a matrix equation

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Keywords

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