Solving Nonlinear Eigenvalue Problems Using A Variant of Newton Method

In this paper, iterative algorithms for finding approximations to the eigenvalues of nonlinear algebraic eigenvalue problems are examined. These algorithms use an efficient numerical procedure for calculating the first and second derivatives of the determinant of the problem. Computational aspects of this procedure as applied to finding all the eigenvalues from a given complex-plane domain in a nonlinear eigenvalue problem are analyzed. The efficiency of the algorithm is demonstrated using an example.