Title: Necessary and sufficient conditions for orthogonal similarity transformations to obtain the Arnoli(Lanczos)-Ritz values
Authors: Vandebril, Raf ×
Van Barel, Marc #
Issue Date: Apr-2006
Publisher: Elsevier science inc
Series Title: Linear Algebra and Its Applications vol:414 issue:2-3 pages:435-444
Abstract: It is a well-known fact that while reducing a symmetric matrix into a similar tridiagonal one, the already tridiagonal matrix in the partially reduced matrix has as eigenvalues the Lanczos-Ritz values. This behavior is also shared by the reduction algorithm which transforms symmetric matrices via orthogonal similarity transformations to semiseparable form. Moreover also the orthogonal reduction to Hessenberg form has a similar behavior with respect to the Arnoldi-Ritz values.

In this paper we investigate the orthogonal similarity transformations creating this behavior. Two easy conditions are derived, which provide necessary and sufficient conditions, such that the partially reduced matrices have the desired convergence behavior. The conditions are easy to check as they demand that in every step of the reduction algorithm two particular matrices need to have a zero block.
ISSN: 0024-3795
Publication status: published
KU Leuven publication type: IT
Appears in Collections:Numerical Analysis and Applied Mathematics Section
× corresponding author
# (joint) last author

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