Numerische Mathematik

, Volume 95, Issue 2, pp 337–345 | Cite as

On an alternative to Gerschgorin circles and ovals of Cassini



An alternative to Gerschgorin circles for the localization of the real eigenvalues of a real matrix was studied in [8]. In this paper we present a similar alternative to the Brauer's theorem on ovals of Cassini.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Brauer, A.: Limits for the characteristic roots of a matrix II. Duke Math. J. 14, 21–26 (1947)MathSciNetMATHGoogle Scholar
  2. 2.
    Brualdi, R.: Matrices, eigenvalues and directed graphs. Lin. Multilin. Alg. 11, 143–165 (1982)MathSciNetMATHGoogle Scholar
  3. 3.
    Brualdi, R.A., Ryser, H.J.: Combinatorial matrix theory. Encyclopedia of Mathematics and its applications 39, Cambridge University Press, 1991Google Scholar
  4. 4.
    Carnicer, J.M., Goodman, T.N.T., Peña, J.M.: Linear conditions for positive determinants. Linear Algebra Appl. 292, 39–59 (1999)CrossRefMathSciNetMATHGoogle Scholar
  5. 5.
    Fan K.: Note on M-matrices. Quart. J. Math. Oxford Ser. 11(2), 43–49 (1961)Google Scholar
  6. 6.
    Li, B., Tsatsomeros, T.J.: Doubly diagonally dominant matrices, Linear Algebra Appl. 261, 221–235 (1997)Google Scholar
  7. 7.
    Ostrowski, A.: Über die Determinanten mit überwiegender Hauptdiagonale, Comm. Mat. Helv. 10, 69–96 (1937)MATHGoogle Scholar
  8. 8.
    Peña, J.M.: A class of P-matrices with applications to the localization of the eigenvalues of a real matrix. SIAM J. Matrix Anal. Appl. 22, 1027–1037 (2001), (electronically)CrossRefGoogle Scholar
  9. 9.
    Rump, S.M.: Ill-conditioned matrices are componentwise near to singularity. SIAM Rev. 41, 102–112 (1999)MathSciNetMATHGoogle Scholar
  10. 10.
    Varga, R.S.: Minimal Gerschgorin sets. Pacific J. Math. 15, 719–729 (1965)MATHGoogle Scholar
  11. 11.
    Varga, R.S., Krautstengl, A.: On Geršgorin-type problems and ovals of Cassini. Electron. Trans. Numer. Anal. 8, 15–20 (1999)MathSciNetMATHGoogle Scholar
  12. 12.
    Zhang, X., Gu, D.: A note on Brauer's theorem. Linear Algebra Appl. 196, 163–174 (1994)CrossRefMathSciNetMATHGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2002

Authors and Affiliations

  1. 1.Departamento de Matemática AplicadaUniversidad de ZaragozaZaragozaSpain

Personalised recommendations