Sine transform based preconditioners for symmetric Toeplitz systems

Linear Algebra and Its Applications

Volumn 232, Issue 1-3, 1996, Pages 237-259

  Chan, Raymond H ^a   Ng, Michael K ^a   Wong, C K ^b  

^a CHINESE UNIVERSITY OF HONG KONG   (Hong Kong)

^b UNIVERSITY OF HONG KONG   (Hong Kong)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 21844523518     PISSN: 00243795     EISSN: None     Source Type: Journal    
DOI: 10.1016/0024-3795(94)00049-2     Document Type: Article

References (23)

1. G. Ammar and W. Gragg, Superfast solution of real positive definite Toeplitz system, SIAM J. Matrix Anal. Appl. 9:61-76 (1988).
2. O. Axelsson and V. Barker, Finite Element Solution of Boundary Value Problems: Theory and Computation, Academic, Orlando, Fla., 1983.
3. G. Bergland, A fast Fourier transform algorithm for real-valued series, Comm. ACM 11:703-710 (1968).
4. D. Bini and F. Di Benedetto, A new preconditioner for the parallel solution of positive definite Toeplitz systems, in Second Annual Symposium on Parallel Algorithms and Architecture, Crete, Greece, 1990, pp. 220-223.
5. E. Boman and I. Koltracht, Fast transform based preconditioners for Toeplitz equations, SIAM J. Matrix Anal. Appl. 16:628-645 (1995).
6. T. Chan, An optimal circulant preconditioner for Toeplitz systems, SIAM J. Sci. Statist. Comput. 9:766-771 (1988).
7. R. Chan, The spectrum of a family of circulant preconditioned Toeplitz systems, SIAM J. Numer. Anal. 26:503-506 (1989).
8. R. Chan, Circulant preconditioners for Hermitian Toeplitz systems, SIAM J. Matrix Anal. Appl. 10:542-506 (1989).
9. R. Chan, X. Jin, and M. Yeung, The circulant operator in the Banach algebra of matrices, Linear Algebra Appl. 149:41-53 (1991).
10. R. Chan and T. Chan, Circulant preconditioners for elliptic problems, J. Numer. Linear Algebra Appl. 1:77-101 (1992).
11. R. Chan and C. Wong, Best conditioned circulant preconditioners, Linear Algebra Appl., 218:205-212 (1995).
12. R. Chan and C. Wong, Sine transform based preconditioners for elliptic problems, submitted for publication.
13. E. Cheney, Introduction to Approximation Theory, McGraw-Hill, New York 1966.
14. C. Chui and A. Chan, Application of approximation theory methods to recursive digital filter design, IEEE Trans. Acoustic. Speech Signal Process. 30:18-24 (1982).
15. I. Gohberg and I. Fel'dman, Convolution Equations and Projection Methods for Their solution, Transl. Math. Monographs 41, Amer. Math. Soc., Providence, 1974.
16. U. Grenander and G. Szegö, Toeplitz Forms and their Applications, 2nd ed., Chelsea, New York, 1984.
17. G. Golub and C. Van Loan, Matrix Computations, 2nd ed., Johns Hopkins U. P. Baltimore, 1989.
18. T. Huckle, Circulant and skew-circulant matrices for solving Toeplitz matrix problems, SIAM J. Matrix Anal. Appl. 13:767-777 (1992).
19. T. Huckle, Fast transforms for tridiagonal linear equations, BIT, 34:99-112 (1994).
20. A. Oppenheim and R. Schafer, Discrete-Time Signal Processing, Prentice-Hall, Englewood Cliffs, N.J. 1989.
21. G. Strang, A proposal for Toeplitz matrix calculations, Stud. Appl. Math. 74:171-176 (1986).
22. E. Tyrtyshnikov, Optimal and super-optimal circulant preconditioners, SIAM J. Matrix Anal. Appl. 13:459-473 (1992).
23. P. Yip and K. Rao, Fast decimation-in-time algorithms for a family of discrete sine and cosine transforms, Circuits Systems Signal Process. 3:387-408 (1984).