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Inclusion of the roots of a polynomial based on Gerschgorin's theorem

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C. CarstensenAuthors Info & Claims

Numerische Mathematik, Volume 59, Issue 1

Pages 349 - 360

https://doi.org/10.1007/BF01385785

Published: 01 December 1991 Publication History

Abstract

In this note a new companion matrix is presented which can be interpreted as a product of Werner's companion matrices [13]. Gerschgorin's theorem yields an inclusion of the roots of a polynomial which is best in the sense of [4] and generalizes a result of L. Elsner [5]. This inclusion is better than the one due to W. Börsch-Supan in [1].

References

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Carstensen, C.: On a linear construction of companion matrices. Linear Algebra Appl. (1990) (accepted for publication)

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Elsner, L.: Über Eigenwerteinschließungen mit Hilfe von Gerschgorin-Kreisen. ZAMM50, 381---384 (1970)

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Elsner, L.: A Remark on Simultaneous Inclusions of the Zeros of a Polynomial by Gershgorin's Theorem. Numer. Math.21, 425---427 (1973)

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Klein, P.P.: Über eine Eigenwertaufgabe, die bei der Einschließung von Matrixeigenwerten und Polynomnullstellen durch kleinste isolierte Gerschgorinkreise auftritt. Ph.D. Thesis, TU Clausthal, 1978

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Cited By

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Bini DRobol L(2014)Solving secular and polynomial equationsJournal of Computational and Applied Mathematics10.1016/j.cam.2013.04.037272(276-292)Online publication date: 1-Dec-2014
https://dl.acm.org/doi/10.1016/j.cam.2013.04.037
Rump S(2003)Ten methods to bound multiple roots of polynomialsJournal of Computational and Applied Mathematics10.1016/S0377-0427(03)00381-9156:2(403-432)Online publication date: 15-Jul-2003
https://dl.acm.org/doi/10.1016/S0377-0427%2803%2900381-9
Neumaier A(2003)Enclosing clusters of zeros of polynomialsJournal of Computational and Applied Mathematics10.1016/S0377-0427(03)00380-7156:2(389-401)Online publication date: 15-Jul-2003
https://dl.acm.org/doi/10.1016/S0377-0427%2803%2900380-7

Inclusion of the roots of a polynomial based on Gerschgorin's theorem
1. Mathematics of computing
  1. Mathematical analysis
    1. Numerical analysis

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Numerische Mathematik Volume 59, Issue 1

December 1991

838 pages

ISSN:0029-599X

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Springer-Verlag

Berlin, Heidelberg

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Published: 01 December 1991

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Bini DRobol L(2014)Solving secular and polynomial equationsJournal of Computational and Applied Mathematics10.1016/j.cam.2013.04.037272(276-292)Online publication date: 1-Dec-2014
https://dl.acm.org/doi/10.1016/j.cam.2013.04.037
Rump S(2003)Ten methods to bound multiple roots of polynomialsJournal of Computational and Applied Mathematics10.1016/S0377-0427(03)00381-9156:2(403-432)Online publication date: 15-Jul-2003
https://dl.acm.org/doi/10.1016/S0377-0427%2803%2900381-9
Neumaier A(2003)Enclosing clusters of zeros of polynomialsJournal of Computational and Applied Mathematics10.1016/S0377-0427(03)00380-7156:2(389-401)Online publication date: 15-Jul-2003
https://dl.acm.org/doi/10.1016/S0377-0427%2803%2900380-7

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Are the coefficients of a polynomial well-conditioned functions of its roots?

Perturbation theorems for estimating magnitudes of roots of polynomials

On the convergence condition of generalized root iterations for the inclusion of polynomial zeros

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