Counting eigenvalues in domains of the complex field

Details Counting eigenvalues in domains of the complex field Counting eigenvalues in domains of the complex field

2011-10-21

arxiv.org/abs/1110.4797v2

Mathematics

Numerical Analysis

21 pages

Scientific paper

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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