A robust AINV-type method for constructing sparse approximate inverse preconditioners in factored form

Numerical Linear Algebra with Applications

Volumn 8, Issue 3, 2001, Pages 165-179

  Kharchenko, S A ^a   Kolotilina, L Yu ^b   Nikishin, A A ^a   Yeremin, A Yu ^c  

^a RUSSIAN ACADEMY OF SCIENCES   (Russian Federation)

^b STEKLOV MATHEMATICAL INSTITUTE   (Russian Federation)

^c MOSCOW STATE UNIVERSITY   (Russian Federation)

Author keywords

AINV method; Approximate inverse preconditioners; Positive definite matrices

Indexed keywords

EID: 0442281595     PISSN: 10705325     EISSN: None     Source Type: Journal    
DOI: 10.1002/1099-1506(200104/05)8:3<165::AID-NLA235>3.0.CO;2-9     Document Type: Article

References (25)

1. Kolotilina LYu, Yeremin AYu. Factorized sparse approximate inverse preconditionings. I: theory. SIAM Journal on Matrix Analysis and Applications 1993; 14:45-58.
2. Kolotilina LYu, Yeremin AYu. Factorized sparse approximate inverse preconditionings. II: Solution of 3D FE systems on massively parallel computers. International Journal of High Speed Computing 1995; 7:191-215.
3. Yeremin AYu, Kolotilina LYu, Nikishin AA. Factorized sparse approximate inverse preconditionings. III: iterative construction of preconditioned. Zapiski Nauchnykh Seminaror POMI 1998; 248:17-48 (English translation to appear in Journal of Mathematical Science (USA)).
4. Yeremin AYu, Kolotilina LYu, Nikishin AA. Factorized sparse approximate inverse preconditionings. III: iterative construction of preconditioned. Zapiski Nauchnykh Seminaror POMI 1998; 248:17-48 (English translation to appear in Journal of Mathematical Science (USA)).
5. Kolotilina LYu. Nikishin AA, Yeremin AYu, Factorized sparse approximate inverse preconditionings. IV: simple approaches to rising efficiency. Numerical Linear Algebra with Applications, to appear.
6. Kaporin IE. New convergence results and preconditioning strategies for the conjugate gradient method. Numerical Linear Algebra with Applications 1994; 1:179-210.
7. Benzi M. A direct row-projection method for sparse linear systems. PhD Thesis, Department of Mathematics, North Carolina State University, Rayleigh, NC, 1993.
8. Benzi M, Meyer CD, Tu̇ma M. A sparse approximate inverse preconditioner for the conjugate gradient method, SIAM Journal on Scientific Computing 1996; 17:1135-1149.
9. Benzi M, Tu̇ma M, A comparative study of sparse approximate inverse preconditioners. Applied Numerical Mathematics, to appear.
10. Benzi M, Tu̇ma M. Numerical experiments with two approximate inverse preconditioners. BIT 1998; 38:234-241.
11. Benzi M, Tu̇ma M. Orderings for factorized sparse approximate inverse preconditioners. Technical Report, LA-UR-98-2175, Los Alamos National Laboratory, 1998.
12. Benzi M, Tu̇ma M, A sparse approximate inverse preconditioner for nonsymmetric linear systems. SIAM Journal on Scientific Computing 1998; 19:968-994.
13. Zhang J, A sparse approximate inverse technique for parallel preconditioning general sparse matrices. Technical Report 281-98, Department of Computer Science, University of Kentucky, Lexington, KY, 1998.
14. Saad Y. Iterative Methods for Sparse Linear Systems. PWS Publ. Co.: Boston, 1996.
15. Duff IS, Grimes RG, Lewis JG. Sparse matrix test problems. ACM Transactions on Mathematical Software 1989; 15:1-14.
16. Benzi M. Personal communication, 1999.
17. Kouhia R. http://www.hut.fi/~kouhia.
18. Concus P, Golub GH, O'Leary DP. A generalized conjugate gradient method for the numerical solution of elliptic partial differential equations. In Sparse Matrix Computations Bunch JR, Rose DJ. (eds). Academic Press: New York, 1976; 309-332.
19. Ajiz MA, Jennings A. A robust incomplete Cholesky conjugate gradient algorithm. International Journal for Numerical Methods in Engineering 1984; 20:946-66.
20. George A, Liu J. Computer Solution of Large Sparse Positive Definite Systems. Prentice-Hall: Englewood Cliffs, NJ, 1981.
21. Bridson R, Tang W-P. Ordering anisotropy and factored sparse approximate inverses. SIAM Journal on Scientific Computing 1999, to appear.
22. Benzi M, Cullum JK, Tu̇ma M, Robust approximate inverse preconditioning for the conjugate gradient method. Technical Report, LA-UR-99-2899, Los Alamos 1999.
23. Benzi M, Kouhia R, Tu̇ma M. An assessment of some preconditioning techniques in shell problems. Communications in Numerical Methods and Engineering 1998; 14:897-906.
24. Bridson R.E. Multi-resolution approximate inverses. MD Thesis, University of Waterloo, Waterloo, Ontario, Canada, 1999.
25. Field MR. An efficient parallel preconditioner for the conjugate gradient algorithm. Technical Report HDL-TR-97-175, O'Reilly Institute, Hitachi Dublin Laboratory, 1997.