Gutknecht, Martin
[Other];
Zemke, Jens-Peter M.
[Other]
;
Technische Universität Hamburg-Harburg Institut für Numerische Simulation,
Technische Universität Hamburg-Harburg
Eigenvalue computations based on IDR
- [Elektronische Ressource]
Footnote:
Research Report No. 2010-13 SAM, ETH Zurich
Institut Numerische Simulation Bericht Nr. 145
Unterschiede zwischen demgedruckten Dokument und der elektronischen Ressource können nicht ausgeschlossen werden
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Description:
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.