Toeplitz Preconditioners with block structure for first-order PDEs

Numerical Linear Algebra with Applications

Volumn 3, Issue 1, 1996, Pages 21-44

  Hemmingsson, Lina ^a  

^a UPPSALA UNIVERSITY   (Sweden)

Author keywords

First order PDEs; Iterative methods; Preconditioners; Toeplitz

Indexed keywords

EID: 21844525525     PISSN: 10705325     EISSN: None     Source Type: Journal    
DOI: 10.1002/(SICI)1099-1506(199601/02)3:1<21::AID-NLA68>3.0.CO;2-G     Document Type: Article

References (13)

1. O. Axelsson. A restarted version of a generalized preconditioned conjugate gradient method. Comm. Appl. Numer. Meth., 4, 521+, 1988.
2. O. Axelsson and G. Lindskog. On the eigenvalue distribution of a class of preconditioning methods. Numer. Math., 48, 479+, 1986.
3. R. H. Chan and X.-Q. Jin. A family of block preconditioners for block systems. SIAM. J. Sci. Stat. Comput., 13, 1218+, 1992.
4. 3b. T. F. Chan. An Optimal Circulant Preconditioner for Toeplitz systems. SIAM J. Sci. Stat. Comput., 9, 766+, 1988.
5. J. Guerra and B. Gustafsson. A semi-implicit method for hyperbolic problems with different time-scales. SIAM J. Numer. Anal., 23, 734+, 1986.
6. B. Gustafsson and H. Stoor. Navier-Stokes equations for almost incompressible flow. SIAM J. Numer. Anal., 28, 1523+, 1991.
7. L. Hemmingsson. A fast modified sine transform for solving block-tridiagonal systems with Toeplitz blocks. Numer. Algor., 7, 375+, 1994.
8. S. Holmgren and K. Otto, A comparison of preconditioned iterative methods for nonsymmetric block-tridiagonal systems of equations. Report No. 123 (revised), Department of Scientific Computing, Uppsala University, Sweden, 1990.
9. S. Holmgren and K. Otto. Iterative solution methods and preconditioners for block-tridiagonal systems of equations. SIAM J. Matrix Anal. Appl., 13, 863+, 1992.
10. T. Huckle. Circulant and skewcirculant matrices for solving Toeplitz matrix problems. SIAM J. Matrix Anal. Appl., 13, 767+, 1992.
11. Y. Saad and M. H. Schultz. GMRES: a generalized minimal residual algorithm for solving nonsymmetric linear systems. SIAM J. Sci. Stat. Comput., 7, 856+, 1986.
12. H. Stoor. Numerical Solution of the Navier-Stokes equations for small Mach numbers. Ph.D. thesis, Department of Scientific Computing, Uppsala University, Uppsala, Sweden, 1990.
13. H. A. van der Vorst. Preconditioning by incomplete decompositions. Ph.D. thesis, Rijksuniversiteit Utrecht, Utrecht, The Netherlands, 1982.