Numerical validation of compensated algorithms with stochastic arithmetic

Numerical validation of compensated algorithms with stochastic arithmetic Compensated algorithms consist in computing the rounding errors of individual operations and then adding them later on to the computed result. This makes it possible to increase the accuracy of the computed result efficiently. Computing the rounding error of an individual operation is possible through the use of a so-called error-free transformation. In this article, we show that it is possible to validate the result of compensated algorithms using stochastic arithmetic. We study compensated algorithms for summation, dot product and polynomial evaluation. We prove that the use of the random rounding mode inherent to stochastic arithmetic does not change much the accuracy of compensated methods. This is due to the fact that error-free transformations are no more exact but still sufficiently accurate to improve the numerical quality of results. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Applied Mathematics and Computation Elsevier

Numerical validation of compensated algorithms with stochastic arithmetic

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Publisher
Elsevier
Copyright
Copyright © 2018 Elsevier Inc.
ISSN
0096-3003
eISSN
1873-5649
D.O.I.
10.1016/j.amc.2018.02.004
Publisher site
See Article on Publisher Site

Abstract

Compensated algorithms consist in computing the rounding errors of individual operations and then adding them later on to the computed result. This makes it possible to increase the accuracy of the computed result efficiently. Computing the rounding error of an individual operation is possible through the use of a so-called error-free transformation. In this article, we show that it is possible to validate the result of compensated algorithms using stochastic arithmetic. We study compensated algorithms for summation, dot product and polynomial evaluation. We prove that the use of the random rounding mode inherent to stochastic arithmetic does not change much the accuracy of compensated methods. This is due to the fact that error-free transformations are no more exact but still sufficiently accurate to improve the numerical quality of results.

Journal

Applied Mathematics and ComputationElsevier

Published: Jul 15, 2018

References

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