Large sparse symmetric eigenvalue problems with homogeneous linear constraints: the Lanczos process with inner–outer iterations
✍ Scribed by Gene H. Golub; Zhenyue Zhang; Hongyuan
- Publisher
- Elsevier Science
- Year
- 2000
- Tongue
- English
- Weight
- 200 KB
- Volume
- 309
- Category
- Article
- ISSN
- 0024-3795
No coin nor oath required. For personal study only.
✦ Synopsis
We study inner-outer iteration approach for large eigenproblems using the symmetric eigenproblem with homogeneous linear constraints as a concrete example. The goal is to compute the extreme eigenvalues to certain accuracy with minimum total number of inner iteration steps. We develop two stopping criteria for the inner-outer Lanczos process: variableaccuracy inner-outer Lanczos process and successive inner-outer Lanczos process, and we provide analysis to explain the behavior of these two inner-outer processes. We also present various numerical examples to demonstrate the efficiency and accuracy of these approaches.