Counting eigenvalues in domains of the complex field

Emmanuel Kamgnia (1) , Bernard Philippe (2)

1 UY1 - Université de Yaoundé I
2 SAGE - Simulations and Algorithms on Grids for Environment

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.

Mots clés: eigenvalues; resolvent; determinant; complex logarithm

Domaines: Analyse numérique [math.NA]

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