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

Loading next page...
 
/lp/springer_journal/towards-optimal-use-of-multi-precision-arithmetic-a-remark-WhOCX6CH5m
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

You’re reading a free preview. Subscribe to read the entire article.


DeepDyve is your
personal research library

It’s your single place to instantly
discover and read the research
that matters to you.

Enjoy affordable access to
over 12 million articles from more than
10,000 peer-reviewed journals.

All for just $49/month

Explore the DeepDyve Library

Unlimited reading

Read as many articles as you need. Full articles with original layout, charts and figures. Read online, from anywhere.

Stay up to date

Keep up with your field with Personalized Recommendations and Follow Journals to get automatic updates.

Organize your research

It’s easy to organize your research with our built-in tools.

Your journals are on DeepDyve

Read from thousands of the leading scholarly journals from SpringerNature, Elsevier, Wiley-Blackwell, Oxford University Press and more.

All the latest content is available, no embargo periods.

See the journals in your area

DeepDyve Freelancer

DeepDyve Pro

Price
FREE
$49/month

$360/year
Save searches from
Google Scholar,
PubMed
Create lists to
organize your research
Export lists, citations
Read DeepDyve articles
Abstract access only
Unlimited access to over
18 million full-text articles
Print
20 pages/month
PDF Discount
20% off