Preconditioned GMRES methods with incomplete Givens orthogonalization method for large sparse least-squares problems
✍ Scribed by Jun-Feng Yin; Ken Hayami
- Publisher
- Elsevier Science
- Year
- 2009
- Tongue
- English
- Weight
- 581 KB
- Volume
- 226
- Category
- Article
- ISSN
- 0377-0427
No coin nor oath required. For personal study only.
✦ Synopsis
We propose to precondition the GMRES method by using the incomplete Givens orthogonalization (IGO) method for the solution of large sparse linear least-squares problems. Theoretical analysis shows that the preconditioner satisfies the sufficient condition that can guarantee that the preconditioned GMRES method will never break down and always give the least-squares solution of the original problem. Numerical experiments further confirm that the new preconditioner is efficient. We also find that the IGO preconditioned BA-GMRES method is superior to the corresponding CGLS method for ill-conditioned and singular least-squares problems.