Towards Optimal Use of Multi-Precision Arithmetic: A Remark

Towards Optimal Use of Multi-Precision Arithmetic: A Remark If standard-precision computations do not lead to the desired accuracy, then it is reasonable to increase precision until we reach this accuracy. What is the optimal way of increasing precision? One possibility is to choose a constant q > 1, so that if the precision which requires the time t did not lead to a success, we select the next precision that requires time q ˙ t˙ It was shown that among such strategies, the optimal (worst-case) overhead is attained when q = 2. In this paper, we show that this “time-doubling” strategy is optimal among all possible strategies, not only among the ones in which we always increase time by a constant q > 1. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Reliable Computing Springer Journals

Towards Optimal Use of Multi-Precision Arithmetic: A Remark

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Publisher
Springer Netherlands
Copyright
Copyright © 2006 by Springer Science + Business Media, Inc.
Subject
Mathematics; Numeric Computing; Mathematical Modeling and Industrial Mathematics; Approximations and Expansions; Computational Mathematics and Numerical Analysis
ISSN
1385-3139
eISSN
1573-1340
D.O.I.
10.1007/s11155-006-9007-4
Publisher site
See Article on Publisher Site

Abstract

If standard-precision computations do not lead to the desired accuracy, then it is reasonable to increase precision until we reach this accuracy. What is the optimal way of increasing precision? One possibility is to choose a constant q > 1, so that if the precision which requires the time t did not lead to a success, we select the next precision that requires time q ˙ t˙ It was shown that among such strategies, the optimal (worst-case) overhead is attained when q = 2. In this paper, we show that this “time-doubling” strategy is optimal among all possible strategies, not only among the ones in which we always increase time by a constant q > 1.

Journal

Reliable ComputingSpringer Journals

Published: Jul 29, 2006

References

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