Stopping criteria, forward and backward errors for perturbed asynchronous linear fixed point methods in finite precision

This paper deals with perturbed linear fixed point methods in the presence of round-off errors. Successive approximations as well as the more general asynchronous iterations are treated. Forward and backward error estimates are presented, and these are used to propose theoretical stopping criteria f...

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Bibliographic Details
Published in:IMA journal of numerical analysis 2005-07, Vol.25 (3), p.429-442
Main Authors: Miellou, J. C., Spiteri, P., El Baz, D.
Format: Article
Language:English
Subjects:
approximate contraction
asynchronous iterations
backward errors
Computer Science
Distributed, Parallel, and Cluster Computing
Error analysis
Exact sciences and technology
fixed point methods
forward errors
Mathematics
Numerical Analysis
Numerical analysis. Scientific computation
Numerical approximation
parallel algorithms
round-off errors
Sciences and techniques of general use
stopping criterion
successive approximation methods
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Summary:This paper deals with perturbed linear fixed point methods in the presence of round-off errors. Successive approximations as well as the more general asynchronous iterations are treated. Forward and backward error estimates are presented, and these are used to propose theoretical stopping criteria for these methods. In the case of asynchronous iterations, macro-iterations are used as a tool in order to obtain estimates.
ISSN:0272-4979
1464-3642
DOI:10.1093/imanum/dri005