Name
Abstract | ||
|---|---|---|
It is well-known that many Krylov solvers for linear systems, eigenvalue problems, and singular value decomposition problems
have very simple and elegant formulas for residual norms. These formulas not only allow us to further understand the methods
theoretically but also can be used as cheap stopping criteria without forming approximate solutions and residuals at each
step before convergence takes place. LSQR for large sparse linear least squares problems is based on the Lanczos bidiagonalization
process and is a Krylov solver. However, there has not yet been an analogously elegant formula for residual norms. This paper
derives such kind of formula. In addition, the author gets some other properties of LSQR and its mathematically equivalent
CGLS. |
Year | DOI | Venue |
|---|---|---|
2010 | 10.1007/s11424-010-7190-1 | J. Systems Science & Complexity |
Keywords | Field | DocType |
least squares,normal equations.,lsqr,cgls,lanczos bidiagonalization,normal equations,krylov subspace,linear system,least square,singular value decomposition | Least squares,Krylov subspace,Singular value decomposition,Mathematical optimization,Lanczos resampling,Linear system,Bidiagonalization,Non-linear least squares,Linear least squares,Mathematics | Journal |
Volume | Issue | ISSN |
23 | 4 | 15597067 |
Citations | PageRank | References |
2 | 0.38 | 3 |
Authors | ||
2 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Zhongxiao Jia | 1 | 121 | 18.57 |
| Zhongxiao Jia | 2 | 121 | 18.57 |