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Title: Eigenvalue computations based on IDR
Language: English
Authors: Gutknecht, Martin 
Zemke, Jens-Peter M.  
Keywords: Induzierte Dimensions-Reduktion; Krylov space method; iterative method; induced dimension reduction; large nonsymmetric eigenvalue problem
Issue Date: May-2010
Abstract (english): 
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.
DOI: 10.15480/882.789
Institute: Mathematik E-10 
Document Type: Preprint
Part of Series: Preprints des Institutes für Mathematik 
Volume number: 145
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