A block constant approximate inverse for preconditioning large linear systems

SIAM Journal on Matrix Analysis and Applications

Volumn 24, Issue 3, 2003, Pages 822-851

  Guillaume, Ph ^a   Huard, A ^a   Le Calvez, C ^a  

^a INSTITUT DE MATHÉMATIQUES DE TOULOUSE   (France)

Author keywords

Approximate inverse; Fast multipole methods; Multigrid methods; Preconditioning

Indexed keywords

EID: 0042415184     PISSN: 08954798     EISSN: None     Source Type: Journal    
DOI: 10.1137/S0895479802401515     Document Type: Article

References (32)

1. O. AXELSSON, Iterative Solution Methods, Cambridge University Press, Cambridge, UK, 1994.
2. M. W. BENSON AND P. O. FREDERICKSON, Iterative solution of large sparse linear systems arising in certain multidimensional approximation problems, Util. Math., 22 (1982), pp. 127-140.
3. J. H. BRAMBLE, J. E. PASCIAK, AND J. XU, Parallel multilevel preconditioners, Math. Comp., 55 (1990), pp. 1-22.
4. R. BRAMLEY AND V. MEÑKOV, Low Rank Off-Diagonal Block Preconditioners for Solving Sparse Linear Systems on Parallel Computers, Tech. Rep. 446, Department of Computer Science, Indiana University, Bloomington, IN, 1996.
5. J. CARRIER, L. GREENGARD, AND V. ROKHLIN, A fast adaptive multipole algorithm for particle simulations, SIAM J. Sci. Statist. Comput., 9 (1988), pp. 669-686.
6. E. CHOW AND Y. SAAD, Approximate inverse preconditioners via sparse-sparse iterations, SIAM J. Sci. Comput., 19 (1998), pp. 995-1023.
7. P. CONCUS, G. GOLUB, AND G. MEURANT, Block preconditioning for the conjugate gradient method, SIAM J. Sci. Statist. Comput., 6 (1985), pp. 220-252.
8. J. D. F. COSGROVE AND J. C. DIAS, Fully parallel preconditionings for sparse systems of equations, in Proceedings of the Second Workshop on Applied Computing, S. Uselton, ed., The University of Tulsa, Tulsa, OK, 1988, pp. 29-34.
9. J. D. F. COSGROVE, J. C. DIAS, AND A. GRIEWANK, Approximate inverse preconditioning for sparse linear systems, Int., J. Comput. Math., 44 (1992), pp. 91-110.
10. E. DARVE, Méthodes multipôles rapides: Résolution des équations de Maxwell par formulations intégrales, Thèse de doctorat, l'Université Paris 6, Paris, France, 1999.
11. I. S. DUFF, A. M. ERISMAN, C. W. GEAR, AND J. K. REID, Sparsity structure and Gaussian elimination, ACM SIGNUM Newsletters, 23 (1988), pp. 2-8.
12. T. F. DUPONT, R. P. KENDALL, AND H. H. RACHFORD, An approximate factorization procedure for solving self-adjoint elliptic difference equations, SIAM J. Numer. Anal., 5 (1968), pp. 559-573.
13. N. ENGHETA, W. D. MURPHY, V. ROKHLIN, AND M. S. VASSILIOU, The fast multipole methode (fmm) for electromagnetic scattering problems, IEEE Trans. Antennas Propag., 40 (1992), pp. 634-641.
14. R. P. FEDORENKO, On the speed of convergence of an iteration process, USSR Comput. Math. Math. Phys., 4 (1964), pp. 227-235.
15. L. GIRAUD, On the Numerical Solution of Partial Differential Equations: Iterative Solvers for Parallel Computers, Habilitation à Diriger des Recherches, I.N.P. de Toulouse, Toulouse, France, 2000.
16. A. GREENBAUM, Iterative Methods for Solving Linear Systems, Frontiers Appl. Math. 17, SIAM, Philadelphia, 1997.
17. L. GREENGARD AND V. ROKHLIN, A fast algorithm for particle simulations, J. Comput. Phys., 73 (1987), pp. 325-348.
18. M. GROTE AND H. S. SIMON, Parallel preconditioning and approximate inverse on the Connection Machine, in Proceedings of the Sixth SIAM Conference on Parallel Processing for Scientific Computing, R. Sincovec, ed., SIAM, Philadelphia, 1993, pp. 519-523.
19. I. GUSTAFSSON, A class of 1st order factorization methods, BIT, 18 (1978), pp. 142-156.
20. W. HACKBUSCH AND B. N. KHOROMSKIJ, A sparse ℋ-matrix arithmetic: General complexity estimates, J. Comput. Appl. Math., 125 (2000), pp. 479-501.
21. M. R. HESTENES AND E. L. STIEFEL, Methods of conjugate gradients for solving linear systems, J. Research Nat. Bur. Standards, 49 (1952), pp. 409-436.
22. L. YU. KOLOTINA AND A. YU. YEREMIN, On a family of two-level preconditionings of the incomplete block factorization type, Sov. J. Numer. Anal. Math. Modelling, 1 (1986), pp. 292-320.
23. M. H. LALLEMAND, H. STEVE, AND A. DERVIEUX, Unstructured multigridding by volume agglomeration: Current status, Comput. & Fluids, 21 (1992), pp. 397-433.
24. C. LANCZOS, Solution of systems of linear equations by minimized iterations, J. Research Nat. Bur. Standards, 49 (1952), pp. 33-53.
25. G. MEURANT, Computer Solution of Large Linear Systems, North- Holland, Amsterdam, 1999.
26. A. VAN DE PLOEG, E. F. F. BOTTA, AND F. W. WUBS, Nested grids ILU-decomposition (NGILU), J. Comput. Appl. Math., 66 (1996), pp. 515-526.
27. J. R. POIRIER, Modélisation électromagnétique des effets de rugosité surfacique, Thèse de doctorat, l'INSA Toulouse, Toulouse, France, 2000.
28. A. POTHEN, H. D. SIMON, AND K.-P. LIOU, Partitioning sparse matrices with eigenvectors of graphs, SIAM J. Matrix Anal. Appl., 11 (1990), pp. 430-452.
29. V. ROKHLIN, Rapid solution of integral equations of classical potential theory, J. Comput. Phys., 60 (1985), pp. 187-207.
30. Y. SAAD, Iterative Methods for Sparse Linear Systems, PWS, New York, 1996.
31. H. D. SIMON AND S.-H. TENG, How good is recursive bisection?, SIAM J. Sci. Comput., 18 (1997), pp. 1436-1445.
32. W.-P. TANG AND W. L. WAN, Sparse approximate inverse smoother for multigrid, SIAM J. Matrix Anal. Appl., 21 (2000), pp. 1236-1252.