Some algorithms for solving special tridiagonal block Toeplitz linear systems

Journal of Computational and Applied Mathematics

Volumn 156, Issue 1, 2003, Pages 179-200

  Minchev, Borislav V ^a  

^a UNIVERSITY OF BERGEN   (Norway)

Author keywords

Block Toeplitz matrix; Linear system; Matrix equation; Woodbury's formula

Indexed keywords

ALGORITHMS; COMPUTATIONAL METHODS; MATHEMATICAL MODELS;

TOEPLITZ SYSTEM;

LINEAR EQUATIONS;

ALGORITHM; MATHEMATICAL ANALYSIS;

EID: 0037532899     PISSN: 03770427     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0377-0427(02)00911-1     Document Type: Article

References (15)

1. D. Bini, B. Meini, Solving block banded block Toeplitz systems with structured blocks: new algorithms and open problems, in: Large-scale Scientific Computations of Engineering and Environmental Problems II, Notes on Numerical Fluid Mechanics, Vol. 73, Vieweg, Braunschweig, Wiesbaden, 2000, pp. 15-24.
2. Buzbee B.L. Golub G.H. Nielson C.W. On direct methods for solving Poisson's equations SIAM J. Numer. Anal. 7 1970 627-656
3. Diele F. Lopez L. The use of the factorization of five-diagonal matrices by tridiagonal Toeplitz matrices Appl. Math. Lett. 11 1998 61-69
4. S.M. El-Sayed, Investigation of special matrices and numerical methods for special matrix equations. Ph.D. Thesis, Sofia, 1996 (in Bulgarian).
5. El-Sayed S.M. Ivanov I.G. Petkov M.G. A new modification of the Rojo Method for solving symmetric circulant five-diagonal systems of linear equations Comput. Math. Appl. 35 1998 35-44
6. -1A=Q Linear Algebra Appl. 186 1993 255-275
7. Fiorentino G. Serra S. Multigrid methods for symmetric positive definite block Toeplitz matrices with nonnegative generating functions SIAM J. Sci. Comput. 17 1996 1068-1081
8. Golub G. Van Loan C. Matrix Computation 1989 The Johns Hopkins University Press Baltimore, MD
9. Guo C.-H. Lancaster P. Iterative solution of two matrix equations Math. Comput. 68 1999 1589-1603
10. -1 A=I, Math. Comput., submitted.
11. I. Ivanov, B. Mintchev, A method for solving special circulant pentadiagonal linear system, in: Large-scale Scientific Computations of Engineering and Environmental Problems II, Notes on Numerical Fluid Mechanics, Vol. 73, Vieweg, Braunschweig, Wiesbaden, 2000, pp. 144-151.
12. B. Meini, Matrix Equations and Structures: Efficient Solution of Special Discrete Algebraic Riccati Equations, in: Second Conference on Numerical Analysis and Applications, Lecture Notes in Computer Science 1988, Springer, Berlin, 2000, pp. 578-585. http://link.springer.de/link/service/series/0558/tocs/t1988.htm
13. Rissanen J. Solution of linear equations with Hancel and Toeplitz matrices Numer. Math. 22 1974 361-366
14. Rojo O. A new method for solving symmetric circulant tridiagonal systems of linear equations Comput. Math. Appl. 20 1990 61-67
15. Zhan X. Computing the extremal positive definite solutions of a matrix equation SIAM J. Sci. Comput. 17 1996 1167-1174