article

Free access

Reducibility Among Floating-Point Graphs

Authors:

Donald B. Johnson,

Webb Miller,

Brian Minnihan,

Celia WrathallAuthors Info & Claims

Journal of the ACM (JACM), Volume 26, Issue 4

Pages 739 - 760

https://doi.org/10.1145/322154.322164

Published: 01 October 1979 Publication History

PDF eReader

References

[1]

Ano, A, AND ULLMAN, J The Theory of Parsing, Translation, and Complhng, VoL ii. Prentice-Hall, Englewood Chffs, N J, 1973

Crossref

Google Scholar

[2]

BAUER, F Computational graphs and rounding error SlAM J. Numer Anal 11 (1974), 87-96.

Google Scholar

[3]

BREUER, M Generation of optimal code for expressions via factonzatlon. Comm. A CM 12, 6 (June 1969), 333-340

Crossref

Google Scholar

[4]

BRows, W A reahsttc model of floatmg-pomt computation In Mathematical Software Iii, J Rice, Ed, Academic Press, New York, 1977, pp. 343-360

Google Scholar

[5]

DORN, W, AND MCCRACKEN, D Numerical Methods with Fortran IV Case Studws. Wiley, New York, 1972

Crossref

Google Scholar

[6]

FATEMAN, R Optimal code for senal and parallel computation Comm A CM 12, 12 (Dec 1969), 694-695

Crossref

Google Scholar

[7]

LARSON, J., AND SAMEH, A Efficient calculanon of the effects of roundoff errors. A CM Trans. Math. Software 4, 3 (Sept 1978), 228-236

Crossref

Google Scholar

[8]

MILLER, W Graph transformations for roundoff analysis SIAM J Comping 5 (1976), 204-216

Google Scholar

[9]

MILLER, W Roundoff analysis by direct companson of two algorithms. SIAM J. Numer. Anal 13 (1976), 382-392

Google Scholar

[10]

MILLER, W. Roundoff analyses and sparse data. Numer. Math. 29 (1977), 37-43

Google Scholar

[11]

MILLER, W., AND SPOONER, D Sogtwar~ for roundoff analysis, ii. ACM Trans. Math Software 4, 4 (Dec. 1978), 369--387.

Crossref

Google Scholar

[12]

MILLER, W., AND WRATHALL, C. Software for RoundoffAnalysis of Matrix Algorithms. Academic Press, New York, 1979

Google Scholar

[13]

WILKINSON, J. Rounding Errors in Algebraic Processes. Premtice-HaH, Englewood Cliffs, N.J., 1963.

Crossref

Google Scholar

Cited By

View all

Hulshof Bvan Hulzen J(2005)Automatic error cumulation controlEUROSAM 8410.1007/BFb0032848(260-271)Online publication date: 10-Jun-2005
https://doi.org/10.1007/BFb0032848
van Hulzen JHulshof BGates Bvan Heerwaarden M(1989)A code optimization package for REDUCEProceedings of the ACM-SIGSAM 1989 international symposium on Symbolic and algebraic computation10.1145/74540.74561(163-170)Online publication date: 17-Jul-1989
https://dl.acm.org/doi/10.1145/74540.74561
Gonzalez TJa’Ja’ J(1982)Evaluation of Arithmetic Expressions with Algebraic IdentitiesSIAM Journal on Computing10.1137/021105411:4(633-662)Online publication date: 1-Nov-1982
https://dl.acm.org/doi/10.1137/0211054
Show More Cited By

Index Terms

Reducibility Among Floating-Point Graphs
1. Mathematics of computing
  1. Discrete mathematics
2. Theory of computation
  1. Computational complexity and cryptography
    1. Problems, reductions and completeness

Recommendations

Comparability Graphs Among Cover-Incomparability Graphs
Algorithms and Discrete Applied Mathematics
Abstract
Comparability graphs and cover-incomparability graphs (C-I graphs) are two interesting classes of graphs from posets. Comparability graph of a poset $P = (V, \leq)$ is a graph with vertex set V and two vertices u and v are adjacent in V if u and v are ...
Decimal Floating-Point Multiplication

Decimal multiplication is important in many commercial applications including financial analysis, banking, tax calculation, currency conversion, insurance, and accounting. This paper presents the design of two decimal floating-point multipliers: one ...
Hardware Designs for Decimal Floating-Point Addition and Related Operations

Decimal arithmetic is often used in commercial, financial, and Internet-based applications. Due to the growing importance of decimal floating-point (DFP) arithmetic, the IEEE 754 Draft Standard for Floating-Point Arithmetic (IEEE P754) includes ...

Comments

Please enable JavaScript to view thecomments powered by Disqus.

Information & Contributors

Information

Published In

Publisher

Association for Computing Machinery

New York, NY, United States

Publication History

Published: 01 October 1979

Published in JACM Volume 26, Issue 4

Permissions

Request permissions for this article.

Request Permissions

Check for updates

Qualifiers

Article

Contributors

Other Metrics

View Article Metrics

Bibliometrics & Citations

Bibliometrics

Article Metrics

6
Total Citations
View Citations
375
Total Downloads

Downloads (Last 12 months)41
Downloads (Last 6 weeks)8

Reflects downloads up to 26 Sep 2024

Other Metrics

View Author Metrics

Citations

Cited By

View all

Hulshof Bvan Hulzen J(2005)Automatic error cumulation controlEUROSAM 8410.1007/BFb0032848(260-271)Online publication date: 10-Jun-2005
https://doi.org/10.1007/BFb0032848
van Hulzen JHulshof BGates Bvan Heerwaarden M(1989)A code optimization package for REDUCEProceedings of the ACM-SIGSAM 1989 international symposium on Symbolic and algebraic computation10.1145/74540.74561(163-170)Online publication date: 17-Jul-1989
https://dl.acm.org/doi/10.1145/74540.74561
Gonzalez TJa’Ja’ J(1982)Evaluation of Arithmetic Expressions with Algebraic IdentitiesSIAM Journal on Computing10.1137/021105411:4(633-662)Online publication date: 1-Nov-1982
https://dl.acm.org/doi/10.1137/0211054
Miller W(1981)A remark on gradual underflowEine Bemerkung zum allmählichen UnderflowComputing10.1007/BF0223797927:3(217-225)Online publication date: Sep-1981
https://doi.org/10.1007/BF02237979
(1980)BIBLIOGRAPHYSoftware for Roundoff Analysis of Matrix Algorithms10.1016/B978-0-12-497250-6.50010-8(143-147)Online publication date: 1980
https://doi.org/10.1016/B978-0-12-497250-6.50010-8
Larson JSameh A(1980)Algorithms for roundoff error analysis —A relative error approachComputing10.1007/BF0223781524:4(275-297)Online publication date: Dec-1980
https://doi.org/10.1007/BF02237815

View Options

View options

PDF

View or Download as a PDF file.

PDF

eReader

View online with eReader.

eReader

Get Access

Login options

Check if you have access through your login credentials or your institution to get full access on this article.

References

Cited By

Index Terms

Recommendations

Comparability Graphs Among Cover-Incomparability Graphs

Decimal Floating-Point Multiplication

Hardware Designs for Decimal Floating-Point Addition and Related Operations

Comments

Information

Published In

Publisher

Publication History

Permissions

Check for updates

Qualifiers

Contributors

Other Metrics

Bibliometrics

Article Metrics

Other Metrics

Citations

Cited By

View options

PDF

eReader

Get Access

Login options

Full Access

Figures

Other

Share

Share this Publication link

Share on social media

Affiliations