, Volume 12, Issue 1, pp 125-149

An adaptive Richardson iteration method for indefinite linear systems

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Abstract

An adaptive Richardson iteration method is presented for the solution of large linear systems of equations with a sparse, symmetric, nonsingular, indefinite matrix. The relaxation parameters for Richardson iteration are chosen to be reciprocal values of Leja points for a compact setK:=[a,b]∪[c,d], where [a,b] is an interval on the negative real axis and [c, d] is an interval on the positive real axis. Endpoints of these intervals are determined adaptively by computing certain modified moments during the iterations. Computed examples show that this adaptive Richardson method can be competitive with the SYMMLQ and the conjugate residual methods, which are based on the Lanczos process.

Communicated by G.H. Golub
Dedicated to Germund Dahlquist on the occasion of his 70th birthday
Research supported in part by the Design and Manufacturing Institute at Stevens Institute of Technology.
Research supported in part by NSF grants DMS-9002884 and DMS-9205531.