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An implementation of the look-ahead Lanczos algorithm for non-Hermitian matrices, part 1The nonsymmetric Lanczos method can be used to compute eigenvalues of large sparse non-Hermitian matrices or to solve large sparse non-Hermitian linear systems. However, the original Lanczos algorithm is susceptible to possible breakdowns and potential instabilities. We present an implementation of a look-ahead version of the Lanczos algorithm which overcomes these problems by skipping over those steps in which a breakdown or near-breakdown would occur in the standard process. The proposed algorithm can handle look-ahead steps of any length and is not restricted to steps of length 2, as earlier implementations are. Also, our implementation has the feature that it requires roughly the same number of inner products as the standard Lanczos process without look-ahead.
Document ID
19920001093
Acquisition Source
Legacy CDMS
Document Type
Contractor Report (CR)
Authors
Freund, Roland W. (Eidgenoessische Technische Hochschule Zurich (Switzerland)., United States)
Gutknecht, Martin H. (Research Inst. for Advanced Computer Science Moffett Field, CA, United States)
Nachtigal, Noel M. (Massachusetts Inst. of Tech. Cambridge., United States)
Date Acquired
September 6, 2013
Publication Date
November 1, 1990
Subject Category
Computer Programming And Software
Report/Patent Number
NAS 1.26:188909
NASA-CR-188909
RIACS-TR-90-45
Accession Number
92N10311
Funding Number(s)
CONTRACT_GRANT: NCC2-387
Distribution Limits
Public
Copyright
Work of the US Gov. Public Use Permitted.

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