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Journal Articles Electronic Transactions on Numerical Analysis Year : 2013

Counting eigenvalues in domains of the complex field

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.
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Dates and versions

hal-00795730 , version 1 (28-02-2013)

Identifiers

  • HAL Id : hal-00795730 , version 1

Cite

Emmanuel Kamgnia, Bernard Philippe. Counting eigenvalues in domains of the complex field. Electronic Transactions on Numerical Analysis, 2013, 40, pp.1-16. ⟨hal-00795730⟩
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