Article,

On the Lánczos method for solving symmetric linear systems with several right-hand sides

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Mathematics of Computation, 48 (178): 651–662 (1987)
DOI: 10.1090/S0025-5718-1987-0878697-3

Abstract

This paper analyzes a few methods based on the Lanczos algorithm for solving large sparse symmetric linear systems with several right-hand sides. The methods examined are suitable for the situation when the right sides are not too different from one another, as is often the case in time-dependent or parameter-dependent problems. We propose a theoretical error bound for the approximation obtained from a projection process onto a Krylov subspace generated from processing a previous right-hand side.

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