A breakdown-free variation of the nonsymmetric Lanczos algorithms
نویسندگان
چکیده
منابع مشابه
A Breakdown-free Variation of the Nonsymmetric Lanczos Algorithms
The nonsymmetric Lanczos tridiagonalization algorithm is essentially the Gram-Schmidt biorthogonalization method for generating biorthogonal bases of a pair of Krylov subspaces. It suffers from breakdown and instability when a pivot at some step is zero or nearly zero, which is often the result of mismatch of the two Krylov subspaces. In this paper, we propose to modify one of the two Krylov su...
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A convergence analysis for the nonsymmetric Lanczos algorithm is presented. By using a tridiagonal structure of the algorithm, some identities concerning Ritz values and Ritz vectors are established and used to derive approximation bounds. In particular, the analysis implies the classical results for the symmetric Lanczos algorithm.
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ژورنال
عنوان ژورنال: Mathematics of Computation
سال: 1994
ISSN: 0025-5718
DOI: 10.1090/s0025-5718-1994-1201072-2