Volume 40, pp. 1-16, 2013.

Counting eigenvalues in domains of the complex field

Emmanuel Kamgnia and Bernard Philippe


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.

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Key words

eigenvalue, resolvent, determinant, complex logarithm

AMS subject classifications


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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