Wavelet sparse approximate inverse preconditioners

BIT Numerical Mathematics

Volumn 37, Issue 3, 1997, Pages 644-660

  Chan, T F ^a   Tang, W P ^b   Wan, W L ^a  

^a UNIVERSITY OF CALIFORNIA   (United States)

^b UNIVERSITY OF WATERLOO   (Canada)

Author keywords

Approximate inverses; Preconditioning; Sparse matrices; Wavelet

Indexed keywords

EID: 0001238648     PISSN: 00063835     EISSN: None     Source Type: Journal    
DOI: 10.1007/BF02510244     Document Type: Article

References (33)

1. O. Axelsson, Iterative Solution Methods, Cambridge University Press, Cambridge, 1994.
2. M. Benson, Iterative Solution of Large Scale Linear Systems, Master's thesis, Lakehead University, Thunder Bay, Ontario, 1973.
3. M. Benson and P. Frederickson, Iterative solution of large sparse linear systems arising in certain multidimensional approximation problems, Utilitas Math., 22 (1982), pp. 127-140.
4. M. Benzi, C. D. Meyer, and M. Tuma, A sparse approximate inverse preconditioner for the conjugate gradient method, SIAM J. Sci. Comput., 17 (1996), pp. 1135-1149.
5. M. Benzi and M. Tuma, A sparse approximate inverse preconditioner for nonsymmetric linear systems, Tech. Rep. TR-PA-96-15, CERFACS, 1996.
6. To appear in SIAM J. Sci. Comput., 1997.
7. G. Beylkin, R. Coifman, and V. Rokhlin, Fast wavelet transforms and numerical algorithms I, Comm. Pure Appl. Math., 44 (1991), pp. 141-184.
8. C. D. Boor, Dichotomies for band matrices, SIAM J. Numer. Anal., 17 (1980), pp. 894-907.
9. F. Canning and J. Scholl, Diagonal preconditioners for the EFIE using a wavelet basis, IEEE Trans. Antennas and Propagation, 44 (1996), pp. 1239-1246.
10. E. Chow and Y. Saad, Approximate inverse techniques for block-partitioned matrices. 1995. To appear in SIAM J. Sci Comput.
11. E. Chow and Y. Saad, Approximate inverse preconditioners for general sparse matrices, Colorado Conference on Iterative Methods, April 5-9, (1994).
12. To appear in SIAM J. Sci. Comput.
13. J. Cosgrove, J. Diaz, and A. Griewank, Approximate inverse preconditionings for sparse linear systems, Internat. J. Comput. Math., 44 (1992), pp. 91-110.
14. I. Daubechies, Orthonormal bases of compactly supported wavelets, Comm. Pure Appl. Math., 41 (1988), pp. 909-996.
15. I. Daubechies, Ten Lectures on Wavelets, CBMS-NSF Series Appl. Math., SIAM, Philadelphia, 1991.
16. S. Demko, Inverses of band matrices and local convergence of spline projections, SIAM J. Numer. Anal., 14 (1977), pp. 616-619.
17. S. Demko, W. Moss, and P. Smith, Decay rates for inverses of band matrices, Math. Comp., 43 (1984), pp. 491-499.
18. V. Eijkhout and B. Polman, Decay rates of inverses of banded m-matrices that are near to Toeplitz matrices, Linear Algebra Applic., 109 (1988), pp. 247-277.
19. B. Engquist, S. Osher, and S. Zhong, Fast wavelet based algorithms for linear evolution equations, SIAM J. Sci. Comput., 15 (1994), pp. 755-775.
20. R. Glowinski, A. Rieder, R. Wells, Jr., and X. Zhou, A wavelet multigrid preconditioner for dirichlet boundary-value problems in general domains, Tech. Rep. TR93-06, Rice Computational Mathematics Laboratory, 1993.
21. N. I. M. Gould and J. A. Scott, On approximate-inverse preconditioners, Tech. Rep. RAL-TR-95-026, The Central Laboratory of the Research Councils, 1995.
22. M. Grote and T. Huckle, Parallel preconditioning with sparse approximate inverses. 1995. To appear in SIAM J. Sci. Comput.
23. M. Grote and H. Simon, Parallel preconditioning and approximate inverses on the connection machine, in Scalable High Performance Computing Conference (SH-PCC), 1992 Williamsburg, VA, IEEE Computer Science Press, 1992, pp. 76-83.
24. M. Grote and H. Simon, Parallel preconditioning and approximate inverses on the connection machine, in Sixth SIAM Conference on Parallel Processing for Scientific Computing II, R. S???? et al, eds., SIAM, 1993, pp. 519-523.
25. L. Kolotilina, A. Nikishin, and A. Yeremin, Factorized sparse approximate inverse (FSAI) preconditionings for solving 3D FE systems on massively parallel computers II, in Iterative Methods in Linear Algebra, Proceedings of the IMACS International Symposium, Brussels, April 2-4, 1991, R. Beauwens and P. Groen, eds., 1992, pp. 311-312.
26. L. Kolotilina and A. Yeremin, Factorized sparse approximate inverse preconditionings I. theory, SIAM J. Matrix Anal. Appl., 14 (1993), pp. 45-58.
27. J. Lifshitz, A. Nikishin, and A. Yeremin, Sparse approximate inverse (FSAI) preconditionings for solving 3D CFD problems on massively parallel computers, in Iterative Methods in Linear Algebra, Proceedings of the IMACS International Symposium, Brussels, April 2-4, 1991, R. Beauwens and P. Groen, eds., 1992, pp. 83-84.
28. G. Meurant, A review on the inverse of symmetric tridiagonal and block tridiagonal matrices, SIAM J. Matrix Anal. Appl., 13 (1992), pp. 707-728.
29. E. Ong, Hierarchical Basis Preconditioners for Second Order Elliptic Problems in Three Dimensions, Ph.D. thesis, University of Washington, Seattle, 1989.
30. W. P. Tang, Effective sparse approximate inverse preconditioners. In preparation, 1995.
31. P. Vassilevski and J. Wang, Stabilizing the hierarchical basis by approximate wavelets, I: Theory, Tech. Rep. 95-47, Dept. of Mathematics, UCLA, 1995.
32. P. Vassilevski and J. Wang, Stabilizing the hierarchical basis by approximate wavelets, II: Implementation and numerical results, Tech. Rep. 95-48, Dept of Mathematics, UCLA, 1995.
33. H. Yserentant, On the multilevel splitting of finite element spaces, Numer. Math., 49 (1986), pp. 379-412.