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Bounds for the round-off errors in the richardson second order method

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Abstract

The application of the Richardson second order iterative method to positive definite, symmetric linear equations is investigated. Absolute and statistical bounds for the round-off error are derived. The statistical theory agrees well with numerical experiments, until the accumulated round-off error becomes of the order of magnitude of the error in the computed solution. After this point the statistical dependence between the local round-off errors makes the observed variances larger than the theoretical variances.

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Authors and Affiliations

  1. Computation Center, Stanford University, Stanford, California

    Gene H. Golub

  2. Department of Mathematics, University of Illinois, Urbana, Illinois

    Gene H. Golub

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  1. Gene H. Golub
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This paper (and the Appendix) describe research carried out while both authors were employed by Space Technology Laboratories, Inc., Los Angeles, California.

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Golub, G.H. Bounds for the round-off errors in the richardson second order method. BIT 2, 212–223 (1962). https://doi.org/10.1007/BF01940168

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  • DOI: https://doi.org/10.1007/BF01940168

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