Name
Abstract | ||
|---|---|---|
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. |
Year | DOI | Venue |
|---|---|---|
2010 | 10.1016/j.cam.2009.11.060 | J. Computational Applied Mathematics |
Keywords | Field | DocType |
convergence property,rational lanczos iteration method,rational lanczos algorithm,different distribution,convergence behavior,numerical example,symmetric eigenvalue problem,numerical algorithm,ritz value,numerical solution,weighted energy problem,krylov subspace,iteration method,eigenvalues,lanczos algorithm,potential theory | Convergence (routing),Mathematical optimization,Potential theory,Lanczos resampling,Eigenvalue distribution,Matrix (mathematics),Iterative method,Mathematical analysis,Lanczos algorithm,Eigenvalues and eigenvectors,Mathematics | Journal |
Volume | Issue | ISSN |
235 | 4 | 0377-0427 |
Citations | PageRank | References |
2 | 0.38 | 9 |
Authors | ||
3 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Andrey Chesnokov | 1 | 7 | 1.20 |
| Karl Deckers | 2 | 46 | 5.92 |
| Marc Van Barel | 3 | 294 | 45.82 |