On the Superlinear Convergence of MINRES

V. Simoncini () and D. B. Szyld ()
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V. Simoncini: Università di Bologna, Dipartimento di Matematica
D. B. Szyld: Temple University (038-16), Department of Mathematics

A chapter in Numerical Mathematics and Advanced Applications 2011, 2013, pp 733-740 from Springer

Abstract: Abstract Quantitative bounds are presented for the superlinear convergence of the MINRES method of Paige and Saunders (SIAM J Numer Anal 12:617–629, 1975) for the solution of sparse linear systems Ax=b, with A symmetric and indefinite. It is shown that the superlinear convergence is observed as soon as the harmonic Ritz values approximate well the eigenvalues of A that are either closest to zero or farthest from zero. This generalizes a well-known corresponding result obtained by van der Sluis and van der Vorst with respect to the Conjugate Gradients method, for A symmetric and positive definite.

Keywords: Superlinear Convergence; Harmonic Ritz Values; MINRES Method; Kuijlaars; Krylov Subspace (search for similar items in EconPapers)
Date: 2013
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-642-33134-3_77

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DOI: 10.1007/978-3-642-33134-3_77

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