Computing the square root and logarithm of a real \(P\)-orthogonal matrix
type: Item
instance of: scholarly article
title: Computing the square root and logarithm of a real \(P\)-orthogonal matrix
zbMATH Open document ID: 1030.65032
DOI: 10.1016/S0168-9274(03)00033-3
author: João R. Cardoso
author: Charles S. Kenney
author: Fátima Silva Leite
published in: Applied Numerical Mathematics
publication date: 2003-08-07T00:00:00Z
review text: The authors consider \(P\)-orthogonal square matrices A such that \(A^TPA=P\) for a fixed real nonsingular matrix \(P\). But most of the results require that \(P\) be symmetric or \(P^T=P^{-1}\) and \(P^2=\pm I\). They present an efficient iterative method for computing the \(P\)-orthogonal factor in the generalized polar decomposition which generalizes Newton's method for polar decomposition. A new iterative method is given for computing the principal square root of a \(P\)-orthogonal matrix. When \(P\) is symmetric positive definite, this method restores the \(P\)-orthogonal properties of the exact square root by computing the nearest \(P\)-orthogonal matrix. New bounds and new estimates for the Padé error of the matrix logarithm improve the existing Briggs-Padé algorithms and adapt them to \(P\)-orthogonal matrices.
reviewed by: Rémi Vaillancourt
Mathematics Subject Classification ID: 65F30
Mathematics Subject Classification ID: 15A24
Mathematics Subject Classification ID: 15A23
zbMATH DE Number: 1961608
zbMATH Keywords: \(P\)-orthoggonal matrices
zbMATH Keywords: generalized polar decomposition
zbMATH Keywords: Padé approximation
zbMATH Keywords: matrix square roots
zbMATH Keywords: matrix logarithm
zbMATH Keywords: error bounds
zbMATH Keywords: iterative method
zbMATH Keywords: Newton's method
zbMATH Keywords: Briggs-Padé algorithms
MaRDI profile type: Publication
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full work available at URL: s0168-9274(03)00033-3
OpenAlex ID: W2014909878
description: scientific article; zbMATH DE number 1961608