On the convergence rate of the QL algorithm with Wilkinson's shift
type: Item
instance of: scholarly article
title: On the convergence rate of the QL algorithm with Wilkinson's shift
zbMATH Open document ID: 0658.65039
DOI: 10.1016/0024-3795(89)90292-9
published in: Linear Algebra and its Applications
publication date: 1989-01-01T00:00:00Z
review text: Let T be a symmetric tridiagonal matrix with distinct eigenvalues, and let \(\lambda_ i\) denote the distinct eigenvalues of T in increasing order. It is proved in this note that if \(\lambda_ i\) satisfies \(| \lambda_{i-1}-\lambda_ i| \neq | \lambda_{i+1}-\lambda_ i|\), then the convergence rate of the QL algorithm with Wilkinson's shift, applied to T, is better than cubic.
Mathematics Subject Classification ID: 65F15
zbMATH DE Number: 4076464
zbMATH Keywords: convergence rate
zbMATH Keywords: symmetric tridiagonal matrix
zbMATH Keywords: QL algorithm with Wilkinson's shift
author: Guo-Dong Zhang
MaRDI profile type: Publication
full work available at URL: 0024-3795(89)90292-9
OpenAlex ID: W2093736832
cites work: A New Proof of Global Convergence for the Tridiagonal $QL$ Algorithm
cites work: Q3719719
cites work: A new shift of the QL algorithm for irreducible symmetric tridiagonal matrices
cites work: A new look at the Lanczos algorithm for solving symmetric systems of linear equations
Wikidata QID: Q127493871
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description: scientific article; zbMATH DE number 4076464