Look-Ahead Procedures for Lanczos-Type Product Methods Based on Three-Term Lanczos Recurrences
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چکیده
منابع مشابه
Look-Ahead Procedures for Lanczos-Type Product Methods Based on Three-Term Lanczos Recurrences
Lanczos-type product methods for solving large sparse non-Hermitian linear systems have as residual polynomials either the squares of the Lanczos polynomials or the products of the latter with another sequence of polynomials, which is normally chosen to enforce some local minimization of the residual norm. In either case, these methods inherit from the underlying Lanczos process the danger of b...
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For the solution of large, sparse, non-Hermitian linear systems, Lanczos-type product methods that are based on the Lanczos three-term recurrence are derived in a systematic way. These methods either square the Lanczos process or combine it with a local minimization of the residual. For them a quasi-minimal residual (QMR) smoothing is proposed that can also be implemented by short-term recurren...
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A breakdown (due to a division by zero) can arise in the algorithms for implementing Lanczos' method because of the non{existence of some formal orthogonal polynomials or because the recurrence relationship used is not appropriate. Such a breakdown can be avoided by jumping over the polynomials involved. This strategy was already used in some algorithms such as the MRZ and its variants. In this...
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ژورنال
عنوان ژورنال: SIAM Journal on Matrix Analysis and Applications
سال: 2000
ISSN: 0895-4798,1095-7162
DOI: 10.1137/s0895479896306744