Block-Toeplitz preconditioning for static and dynamic linear systems

Linear Algebra and Its Applications

Volumn 279, Issue 1-3, 1998, Pages 51-74

  Burrage, K ^a   Jackiewicz, Z ^b   Welfert, B ^b  

^a UNIVERSITY OF QUEENSLAND   (Australia)

^b ARIZONA STATE UNIVERSITY   (United States)

Author keywords

Accelerating of convergence; Iterative methods; Overlapping; Preconditioning; Splitting; Waveform relaxation method

Indexed keywords

EID: 0041375925     PISSN: 00243795     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0024-3795(98)00007-X     Document Type: Article

References (17)

1. O. Nevanlinna, Remarks on Picard-Lindelöf iteration. Part I, BIT 29 (1989) 328-346.
2. U. Miekkala, O. Nevanlinna, Convergence of dynamic iteration method for initial value problems, SIAM J. Sci. Statist. Comput. 8 (1987) 459-482.
3. B. Leimkuhler, Estimating waveform relaxation convergence, SIAM J. Sci. Comput. 14 (1993) 872-889.
4. K. Burrage, Z. Jackiewicz, S.P. Nørsett. R.A. Renaut, Preconditioning waveform relaxation iterations for differential systems, BIT 36 (1996) 54-76.
5. K. Burrage, Parallel and Sequential Methods for Ordinary Differential Equations, Oxford University Press, Oxford, 1995.
6. K. Burrage, Z. Jackiewicz, R.A. Renaut, Waveform relaxation techniques for pseudospectral methods, Numer. Methods Partial Differential Equations 12 (1996) 245-263.
7. R. Chan, The spectrum of a family of circulant preconditioned Toeplitz systems, SIAM J. Numer. Anal. 26 (1989) 503-506.
8. R. Chan, X. Jin, A family of block preconditioners for block systems, SIAM J. Sci. Statist. Comput. 13 (1992) 1218-1235.
9. B. Leimkuhler, Multigrid in time, Report KITCS94-7-1, Kansas Institute for Theoretical and Computational Science, The University of Kansas, 1994.
10. A. Lumsdaine, J. Squyres, M. Reichelt, Waveform Iterative methods for parallel solution of initial value problems, Preprint, Department of Computer Science and Engineering, University of Notre Dame, Notre Dame, 1994.
11. S. Vandewalle, Parallel Multigrid Waveform Relaxation for Parabolic Problems, Teubner, Stuttgart, 1993.
12. T. Freeman, C. Philips, Parallel Numerical Algorithms, Prentice-Hall, New York, 1992.
13. G.H. Golub, C.F. Van Loan, Matrix Computations, John Hopkins University Press, Baltimore, 1989.
14. S. Keras, Waveform relaxation method with Toeplitz operator splitting, DAMTP 1995/NA4, Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Cambridge, England, 1995.
15. S. Keras, Combining domain decomposition with waveform relaxation, DAMTP 1995/NA7, Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Cambridge, England, 1995.
16. M.N. Spijker, Numerical stability: stability estimates and resolvent conditions in the numerical solution of initial value problems, in: Lecture Notes, Department of Mathematics and Computer Science, Leiden University, The Netherlands, 1996.
17. J.K. White, A. Sangiovanni-Vincentelli, Relaxation Techniques for the Simulation of VLSI Circuts, Kluwer Academic Publishers, Dordrecht, 1987.