Scaled Toda-like flows
type: Item
instance of: scholarly article
title: Scaled Toda-like flows
zbMATH Open document ID: 0818.65063
DOI: 10.1016/0024-3795(93)00091-D
author: Moody T. Chu
published in: Linear Algebra and its Applications
publication date: 1995-04-04T00:00:00Z
review text: This very interesting paper discusses the solution of various scaled Toda-like flows of the form \(x' = [x, A\circ x]\), \(x(0) = x_ 0\), where \([ , ]\) is a Lie bracket and \(\circ\) a Hadamard product. The presence of \(A\) allows arbitrary and independent scaling for each element of the matrix \(x\). Various choices of \(A\) are considered which lead, for example, to the continuous power method and the QR algorithm as applied to \(x_ 0\). A convergence theorem is given which allows \(A\) to be chosen in such a way that the convergence of the classical Toda flow is accelerated. This paper concludes with various choices of \(A\) aimed at aggregating the eigenvalues of \(x_ 0\) into blocks.
Mathematics Subject Classification ID: 65L05
Mathematics Subject Classification ID: 37C10
zbMATH DE Number: 740263
zbMATH Keywords: scaled Toda-like flows
zbMATH Keywords: continuous power method
zbMATH Keywords: QR algorithm
zbMATH Keywords: convergence
reviewed by: Kevin Burrage
MaRDI profile type: Publication
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full work available at URL: 0024-3795(93)00091-d
OpenAlex ID: W2043708129
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description: scientific article; zbMATH DE number 740263