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On the Danilewski Method

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Eldon R. HansenAuthors Info & Claims

Journal of the ACM (JACM), Volume 10, Issue 1

Pages 102 - 109

https://doi.org/10.1145/321150.321158

Published: 01 January 1963 Publication History

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References

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Cited By

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Mukhopadhyay AAlagar V(2005)Exact computation of the characteristic polynomial of an integer matrixAlgebraic Algorithms and Error-Correcting Codes10.1007/3-540-16776-5_735(316-324)Online publication date: 4-Jun-2005
https://doi.org/10.1007/3-540-16776-5_735
Faddeev DFaddeeva V(1981)Computational methods of linear algebraJournal of Soviet Mathematics10.1007/BF0108654415:5(531-650)Online publication date: 1981
https://doi.org/10.1007/BF01086544
Howell J(1973)An algorithm for the exact reduction of a matrix to Frobenius form using modular arithmetic. IMathematics of Computation10.1090/S0025-5718-1973-0378381-927:124(887-904)Online publication date: 1973
https://doi.org/10.1090/S0025-5718-1973-0378381-9
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Index Terms

On the Danilewski Method
1. Mathematics of computing
  1. Mathematical analysis
    1. Nonlinear equations
    2. Numerical analysis
      1. Computations on polynomials

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On the Danilewski method for computing the characteristic polynomial
ACM '61: Proceedings of the 1961 16th ACM national meeting

The Danilewski method, as commonly applied, tends to be a very unstable method for finding the characteristic polynomial of a matrix. In this paper we show that, by an appropriate computational procedure, the method seems, in general, to be relatively ...

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Published In

Journal of the ACM Volume 10, Issue 1

Jan. 1963

122 pages

ISSN:0004-5411

EISSN:1557-735X

DOI:10.1145/321150

Issue’s Table of Contents

Publisher

Association for Computing Machinery

New York, NY, United States

Publication History

Published: 01 January 1963

Published in JACM Volume 10, Issue 1

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Cited By

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Mukhopadhyay AAlagar V(2005)Exact computation of the characteristic polynomial of an integer matrixAlgebraic Algorithms and Error-Correcting Codes10.1007/3-540-16776-5_735(316-324)Online publication date: 4-Jun-2005
https://doi.org/10.1007/3-540-16776-5_735
Faddeev DFaddeeva V(1981)Computational methods of linear algebraJournal of Soviet Mathematics10.1007/BF0108654415:5(531-650)Online publication date: 1981
https://doi.org/10.1007/BF01086544
Howell J(1973)An algorithm for the exact reduction of a matrix to Frobenius form using modular arithmetic. IMathematics of Computation10.1090/S0025-5718-1973-0378381-927:124(887-904)Online publication date: 1973
https://doi.org/10.1090/S0025-5718-1973-0378381-9
Van Ness JBoyle JImad F(1965)Sensitivities of large, multiple-loop control systemsIEEE Transactions on Automatic Control10.1109/TAC.1965.109816310:3(308-315)Online publication date: Jul-1965
https://doi.org/10.1109/TAC.1965.1098163
Hart R(1965)Comparison of computer methods of solving the eigenvalue problem of molecular spectroscopyJournal of the Franklin Institute10.1016/0016-0032(65)90228-0279:1(1-10)Online publication date: Jan-1965
https://doi.org/10.1016/0016-0032(65)90228-0
Goldstein RAmundson N(1965)An analysis of chemical reactor stability and control—XaChemical Engineering Science10.1016/0009-2509(65)80033-120:3(195-236)Online publication date: Mar-1965
https://doi.org/10.1016/0009-2509(65)80033-1

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On the Numerical Solution of Fredholm Integral Equations of the First Kind by the Inversion of the Linear System Produced by Quadrature