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Programming Languages: Generation of positive test matrices with known positive spectra

Published: 01 August 1968 Publication History
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  • Abstract

    Sufficient conditions are given for a real matrix to be similar to a positive matrix. This result is used to construct a similarity transformation which, when applied to a particular upper triangular matrix, yields a positive matrix with a preassigned positive spectrum.

    References

    [1]
    BRENNER, J. L. A set of matrices for testing computer programs. Comm. ACM 5, 8 (Aug. 1962), 443-444.
    [2]
    ORTEGA, J. M. Generation of test matrices by similarity transformations. Comm. ACM 7, 6 (June 1964), 377-378.

    Cited By

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    • (2006)Zur Konstruktion invarianter polyedrischer Kegel für gewisse Klassen von reellen Matrizen und deren Ausnutzung für Fehlerabschätzungen beim EigenwertproblemZAMM - Journal of Applied Mathematics and Mechanics / Zeitschrift für Angewandte Mathematik und Mechanik10.1002/zamm.1970050110450:11(665-670)Online publication date: 22-Nov-2006
    • (1970)Certification of algorithm 343 [F1]: eigenvalues and eigenvectors of a real general matrixCommunications of the ACM10.1145/362007.36205013:2(122-124)Online publication date: 1-Feb-1970
    • (1969)Generation of test matrices having certain sign patterns and prescribed positive spectraCommunications of the ACM10.1145/363156.36316112:7(378-379)Online publication date: 1-Jul-1969

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    Published In

    cover image Communications of the ACM
    Communications of the ACM  Volume 11, Issue 8
    Aug. 1968
    48 pages
    ISSN:0001-0782
    EISSN:1557-7317
    DOI:10.1145/363567
    Issue’s Table of Contents
    Permission to make digital or hard copies of all or part of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies bear this notice and the full citation on the first page. Copyrights for components of this work owned by others than ACM must be honored. Abstracting with credit is permitted. To copy otherwise, or republish, to post on servers or to redistribute to lists, requires prior specific permission and/or a fee. Request permissions from [email protected]

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    Association for Computing Machinery

    New York, NY, United States

    Publication History

    Published: 01 August 1968
    Published in CACM Volume 11, Issue 8

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    Author Tags

    1. positive eignevalues
    2. positive matrices
    3. similarity transformation
    4. test matrices

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    • (2006)Zur Konstruktion invarianter polyedrischer Kegel für gewisse Klassen von reellen Matrizen und deren Ausnutzung für Fehlerabschätzungen beim EigenwertproblemZAMM - Journal of Applied Mathematics and Mechanics / Zeitschrift für Angewandte Mathematik und Mechanik10.1002/zamm.1970050110450:11(665-670)Online publication date: 22-Nov-2006
    • (1970)Certification of algorithm 343 [F1]: eigenvalues and eigenvectors of a real general matrixCommunications of the ACM10.1145/362007.36205013:2(122-124)Online publication date: 1-Feb-1970
    • (1969)Generation of test matrices having certain sign patterns and prescribed positive spectraCommunications of the ACM10.1145/363156.36316112:7(378-379)Online publication date: 1-Jul-1969

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