A note on golden means, nonlinear matrix equations and structured doubling algorithms
type: Item
instance of: scholarly article
title: A note on golden means, nonlinear matrix equations and structured doubling algorithms
zbMATH Open document ID: 1226.65032
author: Chun-Yueh Chiang
author: Wen-Wei Lin
author: Eric King-wah Chu
published in: Taiwanese Journal of Mathematics
publication date: 2010-09-02T00:00:00Z
review text: The authors consider two matrix equations \[ BX^{-1}B-X-A=0, \quad XA^{-1}X+X-(B-A)=0, \] where \(0 < A \leq B\). They propose some structured doubling algorithms for computing solutions of these equations and so-called golden means \[ A\natural B = \tfrac{1}{2}[A + A\sharp(4B-3A)], \quad A\bar\natural B = \tfrac{1}{2}[-A + A\sharp(4B-3A)], \] where \(A\sharp B = A^{1/2}(A^{-1/2}BA^{-1/2})^{1/2}A^{1/2}\) [see the paper by \textit{Y.~Lim}, SIAM J. Matrix Anal. Appl. 29, No.~1, 54--66 (2006; Zbl 1171.15014)]. As illustration, some numerical examples are given.
Mathematics Subject Classification ID: 65F30
Mathematics Subject Classification ID: 15A24
Mathematics Subject Classification ID: 26E60
zbMATH DE Number: 5778016
zbMATH Keywords: matrix equation
zbMATH Keywords: matrix golden mean, structured doubling algorithm
zbMATH Keywords: numerical examples
reviewed by: G. V. Demidenko
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.11650/twjm/1500405876
OpenAlex ID: W1607469830
DOI: 10.11650/TWJM/1500405876
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description: scientific article; zbMATH DE number 5778016