Analysis of semi-Toeplitz preconditioners for first-order PDES

SIAM Journal on Scientific Computing

Volumn 17, Issue 1, 1996, Pages 47-64

  Hemmingsson, Lina ^a   Otto, Kurt ^a  

^a UPPSALA UNIVERSITY   (Sweden)

Author keywords

Convergence; Finite difference discretization; First order PDE; Preconditioner; Spectral analysis

Indexed keywords

EID: 0002317316     PISSN: 10648275     EISSN: None     Source Type: Journal    
DOI: 10.1137/0917005     Document Type: Article

References (12)

1. O. AXELSSON, A restarted version of a generalized preconditioned conjugate gradient method, Comm. Appl. Numer. Methods, 4 (1988), pp. 521-530.
2. O. AXELSSON AND G. LINDSKOG, On the eigenvalue distribution of a class of preconditioning methods, Numer. Math., 48 (1986), pp. 479-498.
3. R. W. FREUND, G. H. GOLUB, AND N. M. NACHTIGAL, Iterative solution of linear systems, Acta Numerica (1992), pp. 57-100.
4. J. GUERRA AND B. GUSTAFSSON, A semi-implicit method for hyperbolic problems with different time-scales, SIAM J. Numer. Anal., 23 (1986), pp. 734-749.
5. B. GUSTAFSSON AND H. STOOR, Navier-Stokes equations for almost incompressible flow, SIAM J. Numer. Anal., 28 (1991), pp. 1523-1547.
6. L. HEMMINGSSON, A fast modified sine transform for solving block-tridiagonal systems with Toeplitz blocks, Numer. Algorithms, 7 (1994), pp. 375-389.
7. _, Toeplitz preconditioners with block structure for first-order PDEs, Numer. Linear Algebra Appl., to appear.
8. _, A domain decomposition method for first-order PDEs, SIAM J. Matrix Anal. Appl., 16 (1995), pp. 1241-1267.
9. K. OTTO, Analysis of preconditioners for hyperbolic partial differential equations, SIAM J. Numer. Anal., 33 (1996), to appear.
10. Y. SAAD, Krylov subspace methods for solving large unsymmetric linear systems, Math. Comp., 37 (1981), pp. 105-126.
11. Y. SAAD AND M. H. SCHULTZ, GMRES: A generalized minimal residual algorithm for solving nonsymmetric linear systems, SIAM J. Sci. Statist. Comput., 7 (1986), pp. 856-869.
12. H. A. VAN DER VORST, Preconditioning by incomplete decompositions, Ph.D. thesis, Rijksuniversiteit Utrecht, Utrecht, The Netherlands, 1982.