A note on the fast algorithm for block Toeplitz systems with tensor structure | |
Kou K.-I.; Sin V.-K.; Jin X.-Q. | |
2002-03-10 | |
Source Publication | Applied Mathematics and Computation |
ISSN | 00963003 |
Volume | 126Issue:2-3Pages:187-197 |
Abstract | We study the solutions of block Toeplitz systems Tx = b by using the preconditioned conjugate gradient (PCG) method. Here T = T ⊗ T and T,i = m,n are Toeplitz matrices. In [X. Jin, Appl. Math. Comput. 73 (1995) 115-124], Jin introduced a fast algorithm for these systems by applying the PCG method. This fast algorithm allows a tensor problem to be reduced to a one-dimensional problem. It was proved that if the mn-by-mn system is well conditioned, then the PCG method converges superlinearly and only O(mnlogmn) operations are required in solving the preconditioned system. However, only well-conditioned systems were considered in Jin, 1995. In this paper, we apply this fast algorithm with the {ω}-circulant preconditioners proposed in [D. Potts, G. Steidl, Preconditioners for Ill-Conditioned toeplitz matrices, BIT, to be appeared] to solve the ill-conditioned systems. Numerical results are included to illustrate the effectiveness of the algorithm for solving the preconditioned systems by using the PCG method. An application in image restoration is also given. © 2002 Elsevier Science Inc. All rights reserved. |
Keyword | Block Toeplitz Matrix Image Restoration Pcg Method Preconditioner |
DOI | 10.1016/S0096-3003(00)00150-8 |
URL | View the original |
Indexed By | SCIE |
Language | 英語English |
WOS Research Area | Mathematics |
WOS Subject | Mathematics, Applied |
WOS ID | WOS:000173667100004 |
Publisher | ELSEVIER SCIENCE INC |
Fulltext Access | |
Citation statistics | |
Document Type | Journal article |
Collection | DEPARTMENT OF MATHEMATICS DEPARTMENT OF ELECTROMECHANICAL ENGINEERING |
Affiliation | Universidade de Macau |
First Author Affilication | University of Macau |
Recommended Citation GB/T 7714 | Kou K.-I.,Sin V.-K.,Jin X.-Q.. A note on the fast algorithm for block Toeplitz systems with tensor structure[J]. Applied Mathematics and Computation,2002,126(2-3):187-197. |
APA | Kou K.-I.,Sin V.-K.,&Jin X.-Q..(2002).A note on the fast algorithm for block Toeplitz systems with tensor structure.Applied Mathematics and Computation,126(2-3),187-197. |
MLA | Kou K.-I.,et al."A note on the fast algorithm for block Toeplitz systems with tensor structure".Applied Mathematics and Computation 126.2-3(2002):187-197. |
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