FAST ITERATIVE SOLVERS FOR TOEPLITZ-PLUS-BAND SYSTEMS
Research output: Journal Publications and Reviews › RGC 21 - Publication in refereed journal › peer-review
Author(s)
Detail(s)
| Original language | English |
|---|---|
| Pages (from-to) | 1013-1019 |
| Journal / Publication | SIAM Journal on Scientific Computing |
| Volume | 14 |
| Issue number | 5 |
| Publication status | Published - Sept 1993 |
| Externally published | Yes |
Link(s)
| DOI | DOI |
|---|---|
| Permanent Link | https://scholars.cityu.edu.hk/en/publications/publication(2638ca2b-47ae-4467-ad92-e9d68768668f).html |
Abstract
The authors consider the solutions of Hermitian Toeplitz-plus-band systems (An + Bn)x = b, where An are n-by-n Toeplitz matrices and Bn are n-by-n band matrices with bandwidth independent of n. These systems appear in solving integrodifferential equations and signal processing. However, unlike the case of Toeplitz systems, no fast direct solvers have been developed for solving them. In this paper, the preconditioned conjugate gradient method with band matrices as preconditioners is used. The authors prove that if An is generated by a nonnegative piecewise continuous function and Bn is positive semidefinite, then there exists a band matrix Cn, with bandwidth independent of n, such that the spectra of Cn-1 (An + Bn) are uniformly bounded by a constant independent of n. In particular, we show that the solution of (An + Bn)x = b can be obtained in O(n log n) operations.
Research Area(s)
- Toeplitz matrix, band matrix, generating function, preconditioned conjugate gradient method
Citation Format(s)
FAST ITERATIVE SOLVERS FOR TOEPLITZ-PLUS-BAND SYSTEMS. / CHAN, Raymond H.; NG, Kwok-Po.
In: SIAM Journal on Scientific Computing, Vol. 14, No. 5, 09.1993, p. 1013-1019.
In: SIAM Journal on Scientific Computing, Vol. 14, No. 5, 09.1993, p. 1013-1019.
Research output: Journal Publications and Reviews › RGC 21 - Publication in refereed journal › peer-review
