A one parameter method for the matrix inverse square root
type: Item
instance of: scholarly article
title: A one parameter method for the matrix inverse square root
zbMATH Open document ID: 0938.65072
DOI: 10.1023/A:1022229028633
author: Slobodan Lakić
published in: Applications of Mathematics
publication date: 2000-05-22T00:00:00Z
full work available at URL: https://eudml.org/doc/32989
review text: An inverse square root of a matrix \(A\in L(\mathbb C^m) \) is a solution \(X\in L(\mathbb C^m) \) of the matrix equation \(AX^2=I\) and it is denoted by \(A^{-\frac {1}{2}}\). The inverse square root of \(A\) always exists for a nonsingular matrix \(A\). The author proposes two one-parameter iterative methods and proves that the sequence of iterations constructed by one of this methods converges to the principal \(A^{-\frac {1}{2}}\) if \(A\) has non-negative eigenvalues. Choice of a parameter and numerical stability is discussed. Presented and earlier algorithms published by \textit{N. Sherif} [Computing 46, No. 4, 295-305 (1991; Zbl 0741.65039)] are tested. The four numerical examples show the advantages of parametrized methods.
Mathematics Subject Classification ID: 65F30
zbMATH DE Number: 1450133
zbMATH Keywords: inverse square root
zbMATH Keywords: iterative process
MaRDI profile type: Publication
cites work: Some Metric Inequalities in the Space of Matrices
cites work: Q5579577
cites work: On the computation of a matrix inverse square root
OpenAlex ID: W108519333
Recommended article: An Iterative Method for the Computation of a Matrix Inverse Square Root
Recommended article: Q4896329
Recommended article: On the computation of a matrix inverse square root
Recommended article: Q4357126
Recommended article: Inversion free algorithms for computing the principal square root of a matrix
Recommended article: Fast enclosure for a matrix inverse square root
Recommended article: Q3108023
Recommended article: A numerical method for computing the principal square root of a matrix
Recommended article: THE BINOMIAL METHOD FOR A MATRIX SQUARE ROOT
Recommended article: Iterative methods for computing the matrix square root
description: scientific article; zbMATH DE number 1450133