Abstract
Lanczos methods are remarkably successful for the iterative solution of large, sparse linear systems. The Richardson iteration generates a vector sequence whose convergence to the solution of the linear system can be accelerated using Padé methods. We consider methods of Van der Vorst, Gutknecht and Zhang in the context of vector Padé approximation. This formulation helps to analyse the cause of minimisation breakdown and to avoid it.
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Graves-Morris, P.R. Reliability of Lanczos-Type Product Methods from Perturbation Theory. Reliable Computing 6, 411–428 (2000). https://doi.org/10.1023/A:1009998225359
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DOI: https://doi.org/10.1023/A:1009998225359