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Computational enhancement of an unsymmetric block Lanczos algorithm
Author(s) -
Kim Hyoung M.,
Craig Roy R.
Publication year - 1990
Publication title -
international journal for numerical methods in engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.421
H-Index - 168
eISSN - 1097-0207
pISSN - 0029-5981
DOI - 10.1002/nme.1620300509
Subject(s) - lanczos resampling , biorthogonal system , eigenvalues and eigenvectors , algorithm , block (permutation group theory) , lanczos algorithm , mathematics , computer science , physics , combinatorics , wavelet transform , quantum mechanics , artificial intelligence , wavelet
An unsymmetric block Lanczos algorithm has been employed for the dynamic analysis of a large system which has arbitrary damping and/or repeated (or closely spaced) eigenvalues. In the algorithm development, the right and left Lanczos vectors are all theoretically biorthogonal to each other. However, these vectors may lose the biorthogonality owing to cancellation and roundoff errors. For the unsymmetric case there can be a breakdown, even without numerical errors. This paper describes computational techniques which have led to a robust unsymmetric block Lanczos algorithm.