Volume 40, pp. 1-16, 2013.

Counting eigenvalues in domains of the complex field

Emmanuel Kamgnia and Bernard Philippe

Abstract

A procedure for counting the number of eigenvalues of a matrix in a region surrounded by a closed curve is presented. It is based on the application of the residual theorem. The quadrature is performed by evaluating the principal argument of the logarithm of a function. A strategy is proposed for selecting a path length that insures that the same branch of the logarithm is followed during the integration. Numerical tests are reported for matrices obtained from conventional matrix test sets.

Full Text (PDF) [272 KB]

Key words

eigenvalue, resolvent, determinant, complex logarithm

AMS subject classifications

65F15,65F40,65F50,65E05

Links to the cited ETNA articles

[10]Vol. 18 (2004), pp. 73-80 Ljiljana Cvetkovic, Vladimir Kostic, and Richard S. Varga: A new Geršhgorin-type eigenvalue inclusion set
[24]Vol. 30 (2008), pp. 398-405 Richard S. Varga, Ljiljana Cvetković, and Vladimir Kostić: Approximation of the minimal Geršgorin set of a square complex matrix

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