BTTB preconditioners for BTTB least squares problems
| Autor: | De-Cai Zhang, Fu-Rong Lin |
|---|---|
| Rok vydání: | 2011 |
| Předmět: |
Numerical Analysis
Algebra and Number Theory Preconditioner BTTB matrix Generating function Least squares problem Least squares Square (algebra) PCG method Algebra Matrix (mathematics) Conjugate gradient method Applied mathematics Discrete Mathematics and Combinatorics Geometry and Topology Circulant matrix Image restoration Mathematics |
| Zdroj: | Linear Algebra and its Applications. 434(11):2285-2295 |
| ISSN: | 0024-3795 |
| DOI: | 10.1016/j.laa.2009.10.035 |
| Popis: | In this paper, we consider solving the least squares problem min x ‖ b - T x ‖ 2 by using preconditioned conjugate gradient (PCG) methods, where T is a large rectangular matrix which consists of several square block-Toeplitz–Toeplitz-block (BTTB) matrices and b is a column vector. We propose a BTTB preconditioner to speed up the PCG method and prove that the BTTB preconditioner is a good preconditioner. We then discuss the construction of the BTTB preconditioner. Numerical examples, including image restoration problems, are given to illustrate the efficiency of our BTTB preconditioner. Numerical results show that our BTTB preconditioner is more efficient than the well-known Level-1 and Level-2 circulant preconditioners. |
| Databáze: | OpenAIRE |
| Externí odkaz: |
|
Full Text from ScienceDirect