A new error-free floating-point summation algorithm

Authors:
V. Y. Pan;B. Murphy;G. Qian;R. E. Rosholt
Affiliations:
Department of Mathematics and Computer Science, Lehman College, The City University of New York, Bronx, NY 10468, USA;Department of Mathematics and Computer Science, Lehman College, The City University of New York, Bronx, NY 10468, USA;Ph.D. Program in Computer Science, The City University of New York, New York, NY 10036, USA;Department of Mathematics and Computer Science, Lehman College, The City University of New York, Bronx, NY 10468, USA
Venue:
Computers & Mathematics with Applications
Year:
2009

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Abstract

Summation is a basic operation in scientific computing; furthermore division-free arithmetic computations can be boiled down to summation. We propose a new summation algorithm, which consists of double-precision floating-point operations and outputs the error-free sums. The computational time is proportional to the condition number of the problem, is low according to both our estimates and extensive experiments, and further decreases for producing faithful rounding of the sum, rather than its error-free value.