Escuela Politécnica Superior, Universidad Carlos III de Madrid
Seminar on Orthogonality, Approximation Theory and Applications, Escuela Politécnica Superior, Universidad Carlos III de Madrid, Spain
A numerical algorithm is presented to solve the constrained weighted energy problem from potential theory. As one of the possible applications of this algorithm, the convergence properties of the rational Lanczos iteration method for the symmetric eigenvalue problem are studied. The constrained weighted energy problem characterizes the region containing those eigenvalues that are well approximated by the Ritz values. The region depends on the distribution of the eigenvalues, on the distribution of the poles, and on the ratio between the size of the matrix and the number of iterations. The algorithm presented gives the possibility to find the boundary of this region in an effective way. We give numerical examples for different distributions of poles and eigenvalues and compare the results of our algorithm with the convergence behavior of the explicitly performed rational Lanczos algorithm.