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A Shifted Block Lanczos Algorithm 1: The Block RecurrenceIn this paper we describe a block Lanczos algorithm that is used as the key building block of a software package for the extraction of eigenvalues and eigenvectors of large sparse symmetric generalized eigenproblems. The software package comprises: a version of the block Lanczos algorithm specialized for spectrally transformed eigenproblems; an adaptive strategy for choosing shifts, and efficient codes for factoring large sparse symmetric indefinite matrices. This paper describes the algorithmic details of our block Lanczos recurrence. This uses a novel combination of block generalizations of several features that have only been investigated independently in the past. In particular new forms of partial reorthogonalization, selective reorthogonalization and local reorthogonalization are used, as is a new algorithm for obtaining the M-orthogonal factorization of a matrix. The heuristic shifting strategy, the integration with sparse linear equation solvers and numerical experience with the code are described in a companion paper.
Document ID
19970014139
Acquisition Source
Ames Research Center
Document Type
Other
Authors
Grimes, Roger G.
(Boeing Computer Services Co. Seattle, WA United States)
Lewis, John G.
(Boeing Computer Services Co. Seattle, WA United States)
Simon, Horst D.
(Computer Sciences Corp. Moffett Field, CA United States)
Date Acquired
August 17, 2013
Publication Date
March 2, 1990
Subject Category
Computer Programming And Software
Report/Patent Number
NAS 1.26:203438
RNR-90-003
NAS-CR-203438
Accession Number
97N71091
Funding Number(s)
CONTRACT_GRANT: NAS2-12961
Distribution Limits
Public
Copyright
Work of the US Gov. Public Use Permitted.
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