Zero distributions for discrete orthogonal polynomials
Journal of Computational and Applied Mathematics
Which Eigenvalues Are Found by the Lanczos Method?
SIAM Journal on Matrix Analysis and Applications
Convergence of the Isometric Arnoldi Process
SIAM Journal on Matrix Analysis and Applications
Algorithm 882: Near-Best Fixed Pole Rational Interpolation with Applications in Spectral Methods
ACM Transactions on Mathematical Software (TOMS)
A numerical solution of the constrained energy problem
Journal of Computational and Applied Mathematics
Rational krylov for large nonlinear eigenproblems
PARA'04 Proceedings of the 7th international conference on Applied Parallel Computing: state of the Art in Scientific Computing
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A numerical algorithm is presented to solve the constrained weighted energy problem from potential theory. As one of the possible applications of this algorithm, we study the convergence properties of the rational Lanczos iteration method for the symmetric eigenvalue problem. 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. Our algorithm gives the possibility of finding 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.