Geodesic
Counting eigenvalues in domains of the complex field
Electronic transactions on numerical analysis, Tome 40 (2013), pp. 1-16
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.
Classification : 65F15, 65F40, 65F50, 65E05
Keywords: eigenvalue, resolvent, determinant, complex logarithm 
@article{ETNA_2013__40__a25,
     author = {Kamgnia,  Emmanuel and Philippe,  Bernard},
     title = {Counting eigenvalues in domains of the complex field},
     journal = {Electronic transactions on numerical analysis},
     pages = {1--16},
     year = {2013},
     volume = {40},
     zbl = {1288.65050},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ETNA_2013__40__a25/}
}
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Kamgnia,  Emmanuel; Philippe,  Bernard. Counting eigenvalues in domains of the complex field. Electronic transactions on numerical analysis, Tome 40 (2013), pp. 1-16. http://geodesic.mathdoc.fr/item/ETNA_2013__40__a25/