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Computer Search for Numerical Instability

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Webb MillerAuthors Info & Claims

Journal of the ACM (JACM), Volume 22, Issue 4

Pages 512 - 521

https://doi.org/10.1145/321906.321916

Published: 01 October 1975 Publication History

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References

[1]

FADDEEV, D. K, AND FADDEEVA, V.N. Natural norms in algebraic processes. SIAM J. Namer. Anal, 7 (1970), 520-531.]]

Google Scholar

[2]

HOUSEHOLDER, A. The Theory of Matrices In Numemcal Analysis. Ginn (Blaisdell), Boston, Mass., 1964.]]

Google Scholar

[3]

JOHN, F. Extremum problems with inequalities as subsidiary conditions. In Studies and Essays, presented to R. Courant, Wfley-Interscmnce, New York, 1948, pp. 187-204.]]

Google Scholar

[4]

LEICHTWEISS, K. Ucber die affine Exzentrizitat konvexer Korper. Arch Math. 10 (1959), 187-199.]]

Google Scholar

[5]

MILLER, W. Numerical heuristics m computer-aided roundoff analyms. Research Rep. RC- 4332, IBM Thomas J. Watson Research Center, Yorktown Heights, N.Y, May 2, 1973.]]

Google Scholar

[6]

MILLER, W. Software for roundoff analysis. ACM TOMS i, 2 (June 1975), 108-128.]]

Crossref

Google Scholar

[7]

MILLER, W. Roundoff analysis by direct comparison of two algorithms. Submitted to a technical journal.]]

Google Scholar

[8]

RUDIN, W. Principles of Mathematical Analysis, 2nd ed. McGraw-Hill, New York, 1964]]

Google Scholar

[9]

STEWART, G.W. Introductzon to Matmx Computatzons. Academic Press, New York, 1973.]]

Google Scholar

[10]

WXLKNSON, J., AND REINSCH, C., Eds. Handbook for Automatic Computatzon, Vol. 1l, Lnear Algebra Springer-Verlag, Berlin and New York, 1971.]]

Crossref

Google Scholar

Cited By

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Yehudayoff ACharikar MCohen E(2019)Separating monotone VP and VNPProceedings of the 51st Annual ACM SIGACT Symposium on Theory of Computing10.1145/3313276.3316311(425-429)Online publication date: 23-Jun-2019
https://dl.acm.org/doi/10.1145/3313276.3316311
Miller W(2007)Performing armchair roundoff analyses of statistical algorithmsCommunications in Statistics - Simulation and Computation10.1080/036109178088120747:3(243-255)Online publication date: 27-Jun-2007
https://doi.org/10.1080/03610917808812074
Coppersmith DSchieber B(1999)Lower Bounds on the Depth of Monotone Arithmetic ComputationsJournal of Complexity10.1006/jcom.1998.049415:1(17-29)Online publication date: 1-Mar-1999
https://dl.acm.org/doi/10.1006/jcom.1998.0494
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Index Terms

Computer Search for Numerical Instability
1. Computing methodologies
  1. Symbolic and algebraic manipulation
    1. Symbolic and algebraic algorithms
      1. Linear algebra algorithms
2. Mathematics of computing
  1. Mathematical analysis
    1. Numerical analysis

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Published In

Journal of the ACM Volume 22, Issue 4

Oct. 1975

172 pages

ISSN:0004-5411

EISSN:1557-735X

DOI:10.1145/321906

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Association for Computing Machinery

New York, NY, United States

Publication History

Published: 01 October 1975

Published in JACM Volume 22, Issue 4

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Yehudayoff ACharikar MCohen E(2019)Separating monotone VP and VNPProceedings of the 51st Annual ACM SIGACT Symposium on Theory of Computing10.1145/3313276.3316311(425-429)Online publication date: 23-Jun-2019
https://dl.acm.org/doi/10.1145/3313276.3316311
Miller W(2007)Performing armchair roundoff analyses of statistical algorithmsCommunications in Statistics - Simulation and Computation10.1080/036109178088120747:3(243-255)Online publication date: 27-Jun-2007
https://doi.org/10.1080/03610917808812074
Coppersmith DSchieber B(1999)Lower Bounds on the Depth of Monotone Arithmetic ComputationsJournal of Complexity10.1006/jcom.1998.049415:1(17-29)Online publication date: 1-Mar-1999
https://dl.acm.org/doi/10.1006/jcom.1998.0494
Coppersmith DSchieber B(1992)Lower bounds on the depth of monotone arithmetic computationsProceedings of the 33rd Annual Symposium on Foundations of Computer Science10.1109/SFCS.1992.267763(288-295)Online publication date: 24-Oct-1992
https://dl.acm.org/doi/10.1109/SFCS.1992.267763
Jerrum MSnir M(1982)Some Exact Complexity Results for Straight-Line Computations over SemiringsJournal of the ACM10.1145/322326.32234129:3(874-897)Online publication date: 1-Jul-1982
https://dl.acm.org/doi/10.1145/322326.322341
Ukkonen E(1981)On the calculation of the effects of roundoff errorsACM Transactions on Mathematical Software10.1145/355958.3559597:3(259-271)Online publication date: 1-Sep-1981
https://dl.acm.org/doi/10.1145/355958.355959
Stummel F(1981)Perturbation theory for evaluation algorithms of arithmetic expressionsMathematics of Computation10.1090/S0025-5718-1981-0628707-837:156(435-473)Online publication date: 1981
https://doi.org/10.1090/S0025-5718-1981-0628707-8
(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
Skeel R(1979)Scaling for Numerical Stability in Gaussian EliminationJournal of the ACM10.1145/322139.32214826:3(494-526)Online publication date: 1-Jul-1979
https://dl.acm.org/doi/10.1145/322139.322148
Ukkonen E(1979)An analysis of the effect of rounding errors on the flow of control in numerical processesBIT10.1007/BF0193122919:1(116-133)Online publication date: 1-Mar-1979
https://dl.acm.org/doi/10.1007/BF01931229
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Hopf bifurcation for tearing instability in magnetohydrodynamics, theory and numerical results

Analysis of complicated oscillatory instability phenomena in general power system models

A Numerical Study of FETI Algorithms for Mortar Finite Element Methods

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