The Lanczos algorithm with selective orthogonalization
نویسندگان
چکیده
منابع مشابه
Nested Lanczos : Implicitly Restarting a Lanczos Algorithm Nested Lanczos : Implicitly Restarting a Lanczos Algorithm
In this text, we present a generalisation of the idea of the Implicitly Restarted Arnoldi method to the nonsymmetric Lanczos algorithm, using the two-sided Gram-Schmidt process or using a full Lanczos tridi-agonalisation. The Implicitly Restarted Lanczos method can be combined with an implicit lter. It can also be used in case of breakdown and ooers an alternative for look-ahead.
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The Lanczos algorithm is becoming accepted as a powerful tool for finding the eigenvalues and for solving linear systems of equations. Any practical implementation of the algorithm suffers however from roundoff errors, which usually cause the Lanczos vectors to lose their mutual orthogonality. In order to maintain some level of orthogonality, full reorthogonalization (FRO) and selective orthogo...
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ژورنال
عنوان ژورنال: Mathematics of Computation
سال: 1979
ISSN: 0025-5718,1088-6842
DOI: 10.1090/s0025-5718-1979-0514820-3