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On the Convergence of Diagonal Elements and Asymptotic Convergence Rates for the Shifted Tridiagonal QL Algorithm

On the Convergence of Diagonal Elements and Asymptotic Convergence Rates for the Shifted Tridiagonal QL Algorithm

Year:    1985

Journal of Computational Mathematics, Vol. 3 (1985), Iss. 3 : pp. 252–261

Abstract

The convergence of diagonal elements of an irreducible symmetric triadiagonal matrix under QL algorithm with some kinds of shift is discussed. It is proved that if α1σ→0 and βj→0, j=1,2,...,m, then αjλ_j where λ_j are m eigenvalues of the matrix, and \sigma is the origin shift. The asymptotic convergence rates of three kinds of shift, Rayleigh quotient shift, Wilkinson's shift and RW shift, are analysed.  

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Journal Article Details

Publisher Name:    Global Science Press

Language:    English

DOI:    https://doi.org/1985-JCM-9622

Journal of Computational Mathematics, Vol. 3 (1985), Iss. 3 : pp. 252–261

Published online:    1985-01

AMS Subject Headings:   

Copyright:    COPYRIGHT: © Global Science Press

Pages:    10

Keywords: