On using reinforcement learning to solve sparse linear systems

Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

Volumn 5101 LNCS, Issue PART 1, 2008, Pages 955-964

  Kuefler, Erik ^a   Chen, Tzu Yi ^a  

^a POMONA COLLEGE   (United States)

Author keywords

Iterative methods; Preconditioners; Reinforcement learning

Indexed keywords

EIGENVALUES AND EIGENFUNCTIONS; LINEAR SYSTEMS; REINFORCEMENT LEARNING;

COMPLEX METRICS; COMPUTATIONAL SCIENCES; HEIDELBERG (CO); INTERNATIONAL CONFERENCES; SPARSE LINEAR SYSTEMS; TEST FRAMEWORK; WIDE-RANGE;

REINFORCEMENT;

EID: 47749152316     PISSN: 03029743     EISSN: 16113349     Source Type: Book Series    
DOI: 10.1007/978-3-540-69384-0_100     Document Type: Conference Paper

References (22)

1. Benzi, M.: Preconditioning techniques for large linear systems: A survey. J. of Comp. Physics 182(2), 418-477 (2002)
2. Saad, Y., van der Vorst, H.A.: Iterative solution of linear systems in the 20th century. J. Comput. Appl. Math. 123(1-2), 1-33 (2000)
3. Bhowmick, S., Eijkhout, V., Freund, Y., Fuentes, E., Keyes, D.: Application of machine learning to the selection of sparse linear solvers. International Journal of High Performance Computing Applications (submitted, 2006)
4. Holloway, A.L., Chen, T.-Y.: Neural networks for predicting the behavior of preconditioned iterative solvers. In: Shi, Y., van Albada, G.D., Dongarra, J., Sloot, P.M.A. (eds.) ICCS 2007. LNCS, vol. 4487, pp. 302-309. Springer, Heidelberg (2007)
5. Xu, S., Zhang, J.: Solvability prediction of sparse matrices with matrix structurebased preconditioners. In: Proc. Preconditioning 2005, Atlanta, Georgia (2005)
6. Xu, S., Zhang, J.: SVM classification for predicting sparse matrix solvability with parameterized matrix preconditioners. Technical Report 450-06, University of Kentucky (2006)
7. George, T., Sarin, V.: An approach recommender for preconditioned iterative solvers. In: Proc. Preconditioning 2007, Toulouse, France (2007)
8. Ramakrishnan, N., Ribbens, C.J.: Mining and visualizing recommendation spaces for elliptic PDEs with continuous attributes. ACM Trans. on Math. Softw. 26(2), 254-273 (2000)
9. Sutton, R.S., Barto, A.G.: Reinforcement Learning: An Introduction. MIT Press, Cambridge (1998)
10. Barrett, R., Berry, M., Chan, T.F., Demmel, J., Donato, J., Dongarra, J., Eijkhout, V., Pozo, R., Romine, C., van der Vorst, H.: Templates for the solution of linear systems: Building blocks for iterative methods. SIAM, Philadelphia (1994)
11. Duff, I.S., Koster, J.: The design and use of algorithms for permuting large entries to the diagonal of sparse matrices. SIAM J. Matrix Anal. Appl. 20(4), 889-901 (1999)
12. Duff, I.S., Koster, J.: On algorithms for permuting large entries to the diagonal of a sparse matrix. SIAM J. Matrix Anal. Appl. 22(4), 973-996 (2001)
13. Cuthill, E., McKee, J.: Reducing the bandwidth of sparse symmetric matrices. In: Proc. of the 24th Natl. Conf. of the ACM, pp. 157-172 (1969)
14. Davis, T., Gilbert, J., Larimore, S., Ng, E.: Algorithm 836: COLAMD, a column approximate minimum degree ordering algorithm. ACM Trans. on Math. Softw. 30(3), 377-380 (2004)
15. Davis, T., Gilbert, J., Larimore, S., Ng, E.: A column approximate minimum degree ordering algorithm. ACM Trans. on Math. Softw. 30(3), 353-376 (2004)
16. Chen, T.-Y.: ILUTP.Mem: A space-efficient incomplete LU preconditioner. In: Lagana, A., Gavrilova, M.L., Kumar, V., Mun, Y., Tan, C.J.K., Gervasi, O. (eds.) ICCSA 2004. LNCS, vol. 3046, pp. 31-39. Springer, Heidelberg (2004)
17. Saad, Y., Schultz, M.H.: GMRES: A generalized minimal residual algorithm for solving nonsymmetric linear systems. SIAM J. Sci. Stat. Comput. 7(3), 856-869 (1986)
18. Xu, S., Zhang, J.: A data mining approach to matrix preconditioning problem. Technical Report 433-05, University of Kentucky (2005)
19. Lazzareschi, M., Chen, T.-Y.: Using performance profiles to evaluate preconditioners for iterative methods. In: Gavrilova, M.L., Gervasi, O., Kumar, V., Tan, C.J.K., Taniar, D., Lagana, A., Mun, Y., Choo, H. (eds.) ICCSA 2006. LNCS, vol. 3982, pp. 1081-1089. Springer, Heidelberg (2006)
20. Davis, T.: University of Florida sparse matrix collection. NA Digest 92(42), October 16, 1994 and NA Digest 96(28) July 23, 1996, and NA Digest 97(23) June 7 (1997) http://www.cise.ufi.edu/research/sparse/matrices/
21. Manteuffel, T.A.: An incomplete factorization technique for positive definite linear systems. Mathematics of Computation 34, 473-497 (1980)
22. Kanerva, P.: Sparse Distributed Memory. MIT Press, Cambridge (1988)