A robust ILU with pivoting based on monitoring the growth of the inverse factors

Linear Algebra and Its Applications

Volumn 338, Issue 1-3, 2001, Pages 201-218

  Bollhöfer, Matthias ^a  

^a Universitaets medizin Berlin   (Germany)

Author keywords

65F05; 65F10; 65F50; AINV; Condition estimator; ILU; Pivoting; Sparse approximate inverse; Sparse matrices

Indexed keywords

EID: 0035889740     PISSN: 00243795     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0024-3795(01)00385-8     Document Type: Article

References (28)

1. MATLAB - The language of technical computing. The MathWorks Inc., 1996.
2. Benzi M., Cullum J.K., T ů ma M. Robust approximate inverse preconditioning for the conjugate gradient method. SIAM J. Sci. Comput. 22:2000;1318-1332.
3. Benzi M., Meyer C.D. A direct projection method for sparse linear systems. SIAM J. Sci. Comput. 16(5):1995;1159-1176.
4. Benzi M., Meyer C.D., T ů ma M. A sparse approximate inverse preconditioner for the conjugate gradient method. SIAM J. Sci. Comput. 17:1996;1135-1149.
5. Benzi M., T ů ma M. A sparse approximate inverse preconditioner for nonsymmetric linear systems. SIAM J. Sci. Comput. 19(3):1998;968-994.
6. Bischof C.H. Incremental condition estimation. SIAM J. Matrix Anal. Appl. 11(2):1990;312-322.
7. Bischof C.H., Lewis J.G., Pierce D.J. Incremental condition estimation for sparse matrices. SIAM J. Matrix Anal. Appl. 11(4):1990;644-659.
8. M. Bollhöfer, Y. Saad, On the relations between ILUs and factored approximate inverses, Technical Report umsi-2001-67, Minnesota Supercomputer Institute, University of Minnesota, 2001, (submitted to SIAM Matrix Anal. Appl.).
9. M. Bollhöfer, Y. Saad, A factored approximate inverse preconditioner with pivoting, SIAM Matrix Anal. Appl., to appear.
10. Cline A., Moler C.B., Stewart G., Wilkinson J. An estimate for the condition number of a matrix. SIAM J. Numer. Anal. 16:1979;368-375.
11. T.A. Davis, User's guide for the Unsymmetric-pattern MultiFrontal Package (UMFPACK), Techn. Report TR-95-004, Computer and Information Sciences Department, University of Florida, 1995.
12. Duff I., Erisman A., Reid J. Direct Methods for Sparse Matrices. 1986;Oxford University Press, Oxford, London.
13. Duff I., Grimes R., Lewis J. Sparse matrix test problems. ACM Trans. Math. Software. 15:1989;1-14.
14. I.S. Duff, R.G. Grimes, J.G. Lewis, Users' guide for the Harwell-Boeing sparse matrix collection (release 1), Technical Report RAL-TR-92-086, Rutherford Appleton Laboratory, Oxfordshire, England, 1992.
15. Duff I.S., Reid J. The design of MA48, a code for the direct solution of sparse unsymmetric linear systems of equations. ACM Trans. Math. Software. 22:1996;187-226.
16. Freund R., Golub G., Nachtigal N. Iterative solution of linear systems. Acta Numer. 1992;1-44.
17. George J.A., Liu J.W. Computer Solution of Large Sparse Positive Definite Systems. 1981;Prentice-Hall, Englewood Cliffs, NJ, USA.
18. Golub G., Loan C.V. Matrix Computations. third ed. 1996;The Johns Hopkins University Press, Baltimore, MD.
19. Hestenes M., Stiefel E. Methods of conjugate gradients for solving linear systems. J. Res. Nat. Bur. Standards. 49:1952;409-436.
20. S. Kharchenko, L. Kolotilina, A. Nikishin, A. Yeremin, A reliable AINV-type preconditioning method for constructing sparse approximate inverse preconditioners in factored form, Technical report, Russian Academy of Sciences, Moscow, 1999.
21. Meijerink J., der Vorst H.A.V. An iterative solution method for linear systems of which the coefficient matrix is a symmetric m-matrix. Math. Comp. 31:1977;148-162.
22. Munksgaard N. Solving sparse symmetric sets of linear equations by preconditioned conjugate gradient method. ACM Trans. Math. Software. 6:1980;206-219.
23. National Institute of Standards. Matrix market. available online at http://math.nist.gov/MatrixMarket/.
24. Saad Y. ILUT: a dual treshold incomplete ILU factorization. Numer. Linear Algebra Appl. 1:1994;387-402.
25. Y. Saad, SPARSKIT and sparse examples, NA Digest, 1994.
26. Saad Y. Iterative Methods for Sparse Linear Systems. 1996;PWS Publishing, Boston, MA.
27. Saad Y., Schultz M. GMRES: A generalized minimal residual algorithm for solving nonsymmetric linear systems. SIAM J. Sci. Statist. Comput. 7:1986;856-869.
28. Tismenetsky M. A new preconditioning technique for solving large sparse linear systems. Linear Algebra Appl. 154-156:1991;331-353.