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Approximate solutions and eigenvalue bounds from Krylov subspaces (1995)

Paige, Chris C. ; Parlett, Beresford N. ; van der Vorst, Henk A.

New York, NY [u.a.] : Wiley-Blackwell

Numerical Linear Algebra with Applications 2 (1995), S. 115-133

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Details

ISSN: 1070-5325

Schlagwort(e): Krylov subspace ; Lanczos process ; symmetric matrix ; conjugate gradients ; minimum residual ; Lehmann intervals ; Engineering ; Engineering General

Quelle: Wiley InterScience Backfile Collection 1832-2000

Thema: Mathematik

Notizen: Approximations to the solution of a large sparse symmetric system of equations are considered. The conjugate gradient and minimum residual approximations are studied without reference to their computation. Several different bases for the associated Krylov subspace are used, including the usual Lanczos basis. The zeros of the iteration polynomial for the minimum residual approximation (harmonic Ritz values) are characterized in several ways and, in addition, attractive convergence properties are established. The connection of these harmonic Ritz values to Lehmann's optimal intervals for eigenvalues of the original matrix appears to be new.

Zusätzliches Material: 3 Ill.

Materialart: Digitale Medien

URL: http://dx.doi.org/10.1002/nla.1680020205

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