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 $\alpha_1-\sigma$→0 and $\beta_j$→0, j=1,2,...,m, then $\alpha_j$→$λ_j$ 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