Report 1999-20

Look-Ahead Procedures for Lanczos-Type Product Methods Based on Three-Term Lanczos Recurrences

M.H. Gutknecht and K.J. Ressel

Abstract: Lanczos-type product methods for the solution of large sparse non-Hermitian linear systems either square the Lanczos process or combine it with a local minimization of the residual. They inherit from the underlying Lanczos process the danger of breakdown. For various Lanczos-type product methods that are based on the Lanczos three-term recurrence, look-ahead versions are presented, which avoid such breakdowns or near breakdowns at the cost of a small computational overhead. Different look-ahead strategies are discussed and their efficiency is demonstrated by several numerical examples.

Keywords: Lanczos-type product methods, look-ahead, iterative methods,non-Hermitian matrices, sparse linear systems

Paper: Available as PDF/a> (802 KB) or as hardcopy to order .

Publishing information: SIAM J. Matrix Annal. Appl., 22, p. 213-229, (2000)