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Error linearization as an effective tool for experimental analysis of the numerical stability of algorithms

  • Part II Numerical Mathematics
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Abstract

After introducing briefly the principles of theerror linearization method, which is able to determine the coefficients of the first order error approximation, a collection of examples is presented to demonstrate its efficiency as a test bench for analyzing numerical algorithms. These examples illustrate the propagation of initial errors, the effect of cancellation, the easy location of the most unstable parts of an algorithm, calculation of condition numbers, approximating the statistical behavior of accumulated errors and the convergence of iterative methods.

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Authors and Affiliations

  1. Technical Research Centre of Finland, Computing Services, Revontulentie 7, SF-02120, Espoo 12, Finland

    Seppo Linnainmaa

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  1. Seppo Linnainmaa
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Additional information

Part of this research was done while the author was a visiting scholar at the University of California, Berkeley.

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Linnainmaa, S. Error linearization as an effective tool for experimental analysis of the numerical stability of algorithms. BIT 23, 346–359 (1983). https://doi.org/10.1007/BF01934463

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  • DOI: https://doi.org/10.1007/BF01934463

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