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Eigenvalue computations based on IDR
Citation Link: https://doi.org/10.15480/882.789
Publikationstyp
Preprint
Date Issued
2010-05
Sprache
English
Author(s)
Institut
TORE-DOI
Number in series
145
The Induced Dimension Reduction (IDR) method, which has been introduced as a transpose-free Krylov space method for solving nonsymmetric linear systems, can also be used to determine approximate eigenvalues of a matrix or operator. The IDR residual polynomials are the products of a residual polynomial constructed by successively appending linear smoothing factors and the residual polynomials of a two-sided (block) Lanczos process with one right-hand side and several left-hand sides. The Hessenberg matrix of the OrthoRes version of this Lanczos process is explicitly obtained in terms of the scalars defining IDR by deflating the smoothing factors. The eigenvalues of this Hessenberg matrix are approximations of eigenvalues of the given matrix or operator.
Subjects
Induzierte Dimensions-Reduktion
Krylov space method
iterative method
induced dimension reduction
large nonsymmetric eigenvalue problem
DDC Class
510: Mathematik
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