Orderings for parallel conjugate gradient preconditioners

SIAM Journal on Scientific Computing

Volumn 18, Issue 3, 1997, Pages 854-868

  Stotland, S A ^a   Ortega, J M ^b  

^a Adroit Systems Inc ^*  (United States)

^b University of Virginia ^*  (United States)

Author keywords

Conjugate gradient; Orderings; Parallel; Preconditioner

Indexed keywords

POISSON EQUATION; PRECONDITIONED CONJUGATE GRADIENT METHOD;

CONVERGENCE OF NUMERICAL METHODS; FINITE DIFFERENCE METHOD; LINEAR EQUATIONS; MATHEMATICAL MODELS; MATRIX ALGEBRA; THREE DIMENSIONAL; TWO DIMENSIONAL; VECTORS;

PARALLEL PROCESSING SYSTEMS;

EID: 0031129196     PISSN: 10648275     EISSN: None     Source Type: Journal    
DOI: 10.1137/S1064827593256244     Document Type: Article

References (25)

1. L. ADAMS, Iterative Algorithms for Large Sparse Linear Systems on Parallel Computers, Ph.D. thesis, Department of Applied Mathematics, University of Virginia, Charlottesville, VA, 1982.
2. C. ASHCRAFT AND R. GRIMES, On vectorizing incomplete factorization and SSOR preconditioners, SIAM J. Sci. Statist. Comput., 9 (1988), pp. 122-151.
3. O. AXELSSON AND V. EIJKHOUT, Vectorizable preconditioners for elliptic difference equations in three space dimensions, J. Comput. Appl. Math., 27 (1989), pp. 299-321.
4. E. DAOUDI AND P. MANNEBACK, Parallel ICCG algorithm on distributed memory architecture, in Parallel Processing for Scientific Computing, SIAM, Philadelphia, PA, 1991, pp. 78-83.
5. I. S. DUFF AND G. A. MEURANT, The effect of orderings on preconditioined conjugate gradients, BIT, 29 (1989), pp. 635-647.
6. V. EIJKHOUT, Analysis of parallel incomplete point factorizations, Linear Algebra Appl., 182 (1991), pp. 257-277.
7. S. EISENSTAT. Efficient implementation of a class of conjugate gradient methods, SIAM J. Sci. Statist. Comput., 2 (1981), pp. 1-4.
8. C. FARHAT, Multiprocessors in Computational Mechanics, Ph.D. thesis, Civil Engineering Department, University of California, Berkeley, CA, 1986.
9. L. FREITAG, The RSCG Algorithm on Distributed Memory Architectures, Ph.D. thesis, Department of Applied Mathematics, University of Virginia, Charlottesville, VA, 1992.
10. D. HARRAR, Iterative Solution of Three-Dimensional Generalized Poisson Equations on Vector Computers, Ph.D. thesis, Department of Applied Mathematics, University of Virginia, Charlottesville, VA, 1989.
11. D. HARRAR AND J. ORTEGA, Optimum m-step SSOR preconditioning, J. Appl. Comput. Math., 24 (1988), pp. 195-198.
12. D. HARRAR AND J. M. ORTEGA, Multicoloring with lots of colors, in Proc. Third Internat. Conference Supercomputing, Crete, Greece, 1989, pp. 1-6.
13. D. HARRAR AND J. M. ORTEGA, Solution of three-dimensional generalized poisson equations on vector computers, in Iterative Methods for Large Linear Systems, D. Kincaid and L. Hayes, eds., Academic Press, New York, 1990, pp. 173-191.
14. M. HESTENES AND E. STIEFEL, Methods of conjugate gradients for solving linear systems, J. Res. Nat. Bur. Standards Sect. B, 49 (1952), pp. 409-436.
15. R. MELHEM, Towards efficient implementations of preconditioned conjugate methods on vector supercomputers, Internat. J. Supercomput. Appl., 1 (1987), pp. 70-98.
16. J. M. ORTEGA, Orderings for conjugate gradient preconditionings, SIAM J. Optim., 1 (1991), pp. 565-582.
17. J. M. ORTEGA, Introduction to Parallel and Vector Solution of Linear Systems, Plenum Press, New York, 1988.
18. E. POOLE AND J. ORTEGA, Multicolor ICCG methods for vector computers, SIAM J. Numer. Anal., 24 (1987), pp. 1394-1418.
19. R. SCHREIBER AND W. TANG, Vectorizing the conjugate gradient method, in Proc. Symposium Cyber 205 Applications, Fort Collins, CO, 1982.
20. S. A. STOTLAND, Comparison of Orderings for Parallel Preconditioning, Ph.D. thesis, Department of Applied Mathematics, University of Virginia, Charlottesville, VA, 1993.
21. H. VAN DER VORST, High performance preconditioning, SIAM J. Sci. Statist. Comput., 10 (1989), pp. 1174-1185.
22. H. VAN DER VORST, Large tridiagonal and block tridiagonal linear systems on vector and parallel computers, Parallel Comput., 5 (1987), pp. 45-54.
23. H. VAN DER VORST, A vectorizable variant of some ICCG methods, SIAM J. Sci. Statist. Comput., 3 (1982), pp. 350-356.
24. D. M. YOUNG, Iterative Solution of Large Linear Systems, Academic Press, New York, 1971.
25. T. ZANG, Private communication, 1987.