On Local Roundoff Errors in Floating-Point Arithmetic-Reference-Cited by-同舟云学术

On Local Roundoff Errors in Floating-Point Arithmetic

Published:1973-07 Issue:3 Volume:20 Page:391-398
ISSN:0004-5411
Container-title:Journal of the ACM
language:en
Short-container-title:J. ACM

Author:

Kaneko Toyohisa¹,Liu Bede²

Affiliation:

1. IBM Thomas J Watson Research Center, Yorktown Heights, NY and Princeton University, Princeton, New Jersey

2. Department of Electrical Engineering, Brackett Hall, Engineering Quadrangle, Princeton University, Princeton, New Jersey

Abstract

A bound on the relative error in floating-point addition using a single-precision accumulator with guard digits is derived. It is shown that even with a single guard digit, the accuracy can be almost as good as that using a double-precision accumulator. A statistical model for the roundoff error in double-precision multiplication and addition is also derived. The model is confirmed by experimental measurements.

Publisher

Association for Computing Machinery (ACM)

Subject

Artificial Intelligence,Hardware and Architecture,Information Systems,Control and Systems Engineering,Software

Link

https://dl.acm.org/doi/pdf/10.1145/321765.321771

Reference11 articles.

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2. FORSYTHE G AND MOLhR C B Computer Solutwt~. of L~t~ear Algebra c Systems Prentice- Hall Englewood Cliffs N J 1967.]] FORSYTHE G AND MOLhR C B Computer Solutwt~. of L~t~ear Algebra c Systems Prentice- Hall Englewood Cliffs N J 1967.]]

3. HENRICI P D~screte Vamable Methods ~ Ord~ary D~fferent~al Equatwns Wiley New York 1968.]] HENRICI P D~screte Vamable Methods ~ Ord~ary D~fferent~al Equatwns Wiley New York 1968.]]

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