A numerical method for nonlinear eigenvalue problems using contour integrals

A contour integral method is proposed to solve nonlinear eigenvalue problems numerically. The target equation is F(λ)x=0, where the matrix F(λ) is an analytic matrix function of λ. The method can extract only the eigenvalues λ in a domain defined by the integral path, by reducing the original problem to a linear eigenvalue problem that has identical eigenvalues in the domain. Theoretical aspects of the method are discussed, and we illustrate how to apply of the method with some numerical examples.