Name
Abstract | ||
|---|---|---|
This paper concerns the Rayleigh{Ritz method for computing an approximation to an eigenspaceX of a general matrix A from a subspaceW that contains an approximation to X. The method produces a pair (N; ~ X) that purports to approximate a pair (L;X), where X is a basis for X and AX = XL. In this paper we consider the convergence of (N; ~ X) as the sine of the angle betweenX andW approaches zero. It is shown that under a natural hypothesis | called the uniform separation condition | the Ritz pairs (N; ~ X) converge to the eigenpair (L;X). When one is concerned with eigenvalues and eigenvectors, one can compute certain rened Ritz vectors whose convergence is guaranteed, even when the uniform separation condition is not satised. An attractive feature of the analysis is that it does not assume that A has distinct eigenvalues or is diagonalizable. |
Year | DOI | Venue |
|---|---|---|
2001 | 10.1090/S0025-5718-00-01208-4 | Math. Comput. |
Keywords | Field | DocType |
ritz method,approximating eigenspaces,eigenvalues and eigenvectors,eigenvalues | Rayleigh–Ritz method,Convergence (routing),Rayleigh quotient,Mathematical optimization,Diagonalizable matrix,Subspace topology,Mathematical analysis,Matrix (mathematics),Ritz method,Eigenvalues and eigenvectors,Mathematics | Journal |
Volume | Issue | Citations |
70 | 234 | 26 |
PageRank | References | Authors |
3.24 | 1 | 2 |
Name | Order | Citations | PageRank |
|---|---|---|---|
| Zhongxiao Jia | 1 | 121 | 18.57 |
| G. W. Stewart | 2 | 159 | 42.95 |