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    The Breakdowns of BiCGStab.

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    Publication date
    2002
    Author
    Graves-Morris, Peter R.
    Keyword
    BiCGStab
    BiCG
    Lanczos
    Pivot breakdown
    Lanczos breakdown
    LTPM
    Peer-Reviewed
    Yes
    
    Metadata
    Show full item record
    Abstract
    The 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.
    URI
    http://hdl.handle.net/10454/3726
    Version
    No full-text available in the repository
    Citation
    Graves-Morris, P.R. (2002). The Breakdowns of BiCGStab. Numerical Algorithms. Vol. 29, No. 1-3, pp. 97-105.
    Link to publisher’s version
    http://dx.doi.org/10.1023/A:1014864007293
    Type
    Article
    Collections
    Engineering and Informatics Publications

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