Name
Abstract | ||
|---|---|---|
We make a convergence analysis of the harmonic and refined harmonic extraction versions of Jacobi-Davidson SVD (JDSVD) type methods for computing one or more interior singular triplets of a large matrix A. At each outer iteration of these methods, a correction equation, i.e., inner linear system, is solved approximately by using iterative methods, which leads to two inexact JDSVD type methods, as opposed to the exact methods where correction equations are solved exactly. Accuracy of inner iterations critically affects the convergence and overall efficiency of the inexact JDSVD methods. A central problem is how accurately the correction equations should be solved to ensure that both of the inexact JDSVD methods can mimic their exact counterparts well, that is, they use almost the same outer iterations to achieve the convergence. In this paper, similar to the available results on the JD type methods for large matrix eigenvalue problems, we prove that each inexact JDSVD method behaves like its exact counterpart if all the correction equations are solved with low or modest accuracy during the outer iterations. Based on the theory, we propose practical stopping criteria for inner iterations. Numerical experiments confirm our theory and the effectiveness of the inexact algorithms. |
Year | DOI | Venue |
|---|---|---|
2019 | 10.1137/18M1192019 | SIAM JOURNAL ON SCIENTIFIC COMPUTING |
Keywords | Field | DocType |
singular triplets,JDSVD method,harmonic extraction,refined harmonic extraction,subspace expansion,inner iteration | Convergence (routing),Applied mathematics,Singular value decomposition,Linear system,Iterative method,Matrix (mathematics),Mathematical analysis,Harmonic,Mathematics,Computation | Journal |
Volume | Issue | ISSN |
41 | 3 | 1064-8275 |
Citations | PageRank | References |
1 | 0.36 | 7 |
Authors | ||
2 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Jinzhi Huang | 1 | 2 | 0.72 |
| Zhongxiao Jia | 2 | 121 | 18.57 |