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

Author:
Youcef Saad

Journal:
Math. Comp. **48** (1987), 651-662

MSC:
Primary 65F10; Secondary 65F50

DOI:
https://doi.org/10.1090/S0025-5718-1987-0878697-3

MathSciNet review:
878697

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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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DOI:
https://doi.org/10.1090/S0025-5718-1987-0878697-3

Article copyright:
© Copyright 1987
American Mathematical Society