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A Generalized Kahan-Babuška-Summation-Algorithm

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Abstract

In this article, we combine recursive summation techniques with Kahan-Babuška type balancing strategies [1], [7] to get highly accurate summation formulas. An i-th algorithm have only error beyond 1upl and thus allows to sum many millions of numbers with high accuracy. The additional afford is a small multiple of the naive summation. In addition we show that these algorithms could be modified to provide tight upper and lower bounds for use with interval arithmetic.

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  1. Universität Kassel, Heinrich-Plett-Str. 40 (AVZ), 34132, Kassel, Germany

    A. Klein

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  1. A. Klein
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Klein, A. A Generalized Kahan-Babuška-Summation-Algorithm. Computing 76, 279–293 (2006). https://doi.org/10.1007/s00607-005-0139-x

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  • DOI: https://doi.org/10.1007/s00607-005-0139-x

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