Journal
SIAM JOURNAL ON SCIENTIFIC COMPUTING
Volume 33, Issue 4, Pages 1810-1836Publisher
SIAM PUBLICATIONS
DOI: 10.1137/100787921
Keywords
MINRES; Krylov subspace method; Lanczos process; conjugate-gradient method; minimum-residual method; singular least-squares problem; sparse matrix
Categories
Funding
- National Science Foundation [CCR-0306662]
- NSERC of Canada [OGP0009236]
- Office of Naval Research [N00014-02-1-0076, N00014-08-1-0191]
- AHPCRC
Ask authors/readers for more resources
CG, SYMMLQ, and MINRES are Krylov subspace methods for solving symmetric systems of linear equations. When these methods are applied to an incompatible system (that is, a singular symmetric least-squares problem), CG could break down and SYMMLQ's solution could explode, while MINRES would give a least-squares solution but not necessarily the minimum-length (pseudoinverse) solution. This understanding motivates us to design a MINRES-like algorithm to compute minimum-length solutions to singular symmetric systems. MINRES uses QR factors of the tridiagonal matrix from the Lanczos process (where R is upper-tridiagonal). MINRES-QLP uses a QLP decomposition (where rotations on the right reduce R to lower-tridiagonal form). On ill-conditioned systems (singular or not), MINRES-QLP can give more accurate solutions than MINRES. We derive preconditioned MINRES-QLP, new stopping rules, and better estimates of the solution and residual norms, the matrix norm, and the condition number.
Authors
I am an author on this paper
Click your name to claim this paper and add it to your profile.
Reviews
Recommended
No Data Available