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The Breakdowns of BiCGStab.

By Peter R. Graves-Morris

Abstract

NoThe effects of the three principal possible exact breakdowns which may occur using BiCGStab are discussed. BiCGStab is used to solve large sparse linear systems of equations, such as arise from the discretisation of PDEs. These PDEs often involve a parameter, say . We investigate here how the numerical error grows as breakdown is approached by letting tend to a critical value, say c, at which the breakdown is numerically exact. We found empirically in our examples that loss of numerical accuracy due stabilisation breakdown and Lanczos breakdown was discontinuous with respect to variation of around c. By contrast, the loss of numerical accuracy near a critical value c for pivot breakdown is roughly proportional to |¿c|¿1

Topics: BiCGStab, BiCG, Lanczos, Pivot breakdown, Lanczos breakdown, LTPM
Year: 2002
DOI identifier: 10.1023/A:1014864007293
OAI identifier: oai:bradscholars.brad.ac.uk:10454/3726
Provided by: Bradford Scholars
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