Analysis of parallel preconditioned conjugate gradient algorithms

Informatica

Volumn 16, Issue 3, 2005, Pages 317-332

  Čiegis, Raimondas ^a  

^a VILNIUS GEDIMINAS TECHNICAL UNIVERSITY   (Lithuania)

Author keywords

Incomplete factorization; Parallel algorithms; Preconditioned conjugate gradient method; Scalability analysis

Indexed keywords

EID: 24944561240     PISSN: 08684952     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article

References (28)

1. Akcadogan, C., H. Dag (2003). A parallel implementation of Chebyshev preconditioned conjugate gradient method. In Proceedings of the Second International Symposium on Parallel and Distributed Computing, IEEE, Computer Society. pp. 101-108.
2. Amoura, A., E. Bampis, J. König (1998). Scheduling algorithms for parallel Gaussian elimination with communication costs. IEEE Transactions on Parallel and Distributed Systems, 9(7), 679-686.
3. D'Azevedo, E.F., P.A. Forsyth, W. Tang (1992). Ordering methods for preconditioned conjugate gradient methods applied to unstructured grid problems. SIAM J. Matrix Anal. Appl., 10(4), 567-584.
4. Balay, S., K. Buschelman, V. Eijkhout, W.D. Gropp, D. Kaushik, M.G. Knepley, L. Curfman McInnes, B.F. Smith, H. Zhang (2004). PETSc Users Manual. ANL-95/11 - Revision 2.1.5. Argonne National Laboratory.
5. Blanco, V., P. Gonzalez, J.C. Cabaleiro, D.B. Heras, T.F. Pena, J.J. Pombo, F.F. Rivera (2004). Performance prediction for parallel iterative solvers. The Journal of Supercomputing, 28(2), 177-191.
6. Čiegis, R., A. Dement'ev, G. Šilko (2004). Parallel numerical modelling of short laser pulse compression. Mathematical Modelling and Analysis, 9(2), 115-126.
7. Čiegis, R., A. Jakušev, A. Krylovas, O. Suboč (2005). Parallel algorithms for solution of nonlinear diffusion problems in image smoothing. Mathematicall Modelling and Analysis, 10(2), 155-174.
8. Čiegis, R., V. Starikovičius (2003). Realistic performance tool for the parallel block LU factorization algorithm. Informatica, 14(2), 167-180.
9. Čiegis, R., V.Starikovičius, J. Wasniewski (2000). On the efficiency of scheduling algorithms for parallel Gaussian elimination with communication delays. Lecture Notes in Computer Science, 1947, PARA2000. In
10. T. Surevik, F. Manne, R. Moe, A.H. Gebremedhin (Eds.), The Fifth Workshop on Applied Parallel Computing. Springer, pp. 75-82.
11. Djordjević, G., M. Tošić (1996). A heuristic for scheduling task graphs with communication delays onto multiprocessors. Parallel Computing, 22, 1197-1214.
12. Doi, S., T. Washio (1999). Ordering strategies and related techniques to overcome the trade-off between parallelism and convergence in incomplete factorizations. Parallel Computing, 25, 1995-2014.
13. Duff, I.S., H.A. van der Vorst (1999). Developments and trends in the parallel solution of linear systems. Parallel Computing, 25, 1931-1970.
14. Golub, G.H., Ch. Van Loan (1996). Matrix Computations. The Johns Hopkins University Press, Baltimore.
15. Gupta, A., V. Kumar, A. Sameh (1997). Performance and scalability of preconditioned conjugate gradient methods on parallel computers. IEEE Transactions on Parallel and Distributed Systems, 6 (5), 455-469.
16. Jourbert, W.D., G.F. Carey (1993). PCG: A software package for the iterative solution of linear systems on scalar, vector and parallel computers. In R.F. Sincovec, D.E. Keyes, M.R. Leuze, L.R. Petzold, D.A. Reed (Eds.), Proceedings of the Sixth SIAM Conference on Parallel Processing for Scientific Computing, SIAM. pp. 515-518.
17. Hockney, R. (1991). Performance parameters and benchmarking on supercomputers. Parallel Computing, 17, 1111-1130.
18. Kumar, V., A. Grama, A. Gupta, G. Karypis (1994). Introduction to Parallel Computing: Design and Analysis of Algorithms. Benjamin/Cummings, Redwood City.
19. Lewis, T.G, H. El-Rewini (1992). Introduction to Parallel Computing. Prentice-Hall, Inc.
20. Ma, S. (2004). Comparisons of the parallel preconditioned for large nonsymmetric sparse linear systems on a parallel computer. International Journal of High Speed Computing, 12(1), 55-68.
21. Monga-Made, M. (1995). Ordering strategies for modified block incomplete factorizations. SIAM J. Sci. Stat. Comput., 16, 378-399.
22. Monga-Made, M., H.A. van der Vorst (2001). A generalized domain decomposition paradigm for parallel incomplete LU factorization preconditionings. Future Generation Computer Systems, 17, 925-932.
23. Pardalos, P.M., A. Philips, J.B. Rosen (1992). Topics in Parallel Computing in Mathematical Programming. Science Press.
24. Pardalos, P.M., Sanguthevar Rajasekaran (Eds.) (1999). Advances in Randomized Parallel Computing. Kluwer Academic Publishers.
25. Pardalos, P.M., G. Xue, P.D. Panagiotopoulos (1996). Parallel algorithms for global optimization. In A. Ferreira and P.M. Pardalos (Eds.), Solving Combinatorial Optimization Problems in Parallel: Methods and Techniques. Spinger-Verlag. Lecture Notes in Computer Science, 1054, 233-247.
26. Saad, Y., G. Ching Lo, S. Kuznetsov (1998). PSPARSLIB Users Manual: a Portable Library of Parallel Sparse Iterative Solvers. http://www-users.cs.umn. edu/saad/software/p_sparslib/
27. Samarskii, A.A. (2001). The Theory of Difference Schemes, Marcel Dekker, Inc., New York-Basel.
28. Thiagarajan, G., V. Aravamuthan (2002). Parallelization strategies for element-by-element preconditioned conjugate gradient solver using high-performance Fortran for unstructured finite-element applications on Linux clusters. J. Comp. in Civ. Engrg., 16 (1), 1-10.