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Counting eigenvalues in domains of the complex field

Emmanuel Kamgnia 1 Bernard Philippe 2 
2 SAGE - Simulations and Algorithms on Grids for Environment
Inria Rennes – Bretagne Atlantique , IRISA-D1 - SYSTÈMES LARGE ÉCHELLE
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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Submitted on : Thursday, February 28, 2013 - 6:36:55 PM
Last modification on : Thursday, January 20, 2022 - 5:32:50 PM


  • HAL Id : hal-00795730, version 1


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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