On asynchronous iterations

Journal of Computational and Applied Mathematics

Volumn 123, Issue 1-2, 2000, Pages 201-216

  Frommer, Andreas ^a   Szyld, Daniel B ^b  

^a UNIVERSITY OF WUPPERTAL   (Germany)

^b Temple University   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

ALGORITHMS; APPROXIMATION THEORY; COMPUTER SIMULATION; CONVERGENCE OF NUMERICAL METHODS; INITIAL VALUE PROBLEMS; LINEAR EQUATIONS; MATHEMATICAL MODELS; MATRIX ALGEBRA; NONLINEAR EQUATIONS; PARALLEL PROCESSING SYSTEMS;

ASYNCHRONOUS ITERATIONS; PICARD ITERATION; WAVEFORM RELAXATION METHOD;

ITERATIVE METHODS;

EID: 0034321378     PISSN: 03770427     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0377-0427(00)00409-X     Document Type: Article

References (68)

1. Amitai D., Averbuch A., Israeli M., Itzikowitz S. On parallel asynchronous high-order solutions of parabolic PDEs. Numer. Algorithms. 12:1996;159-192.
2. Amitai D., Averbuch A., Israeli M., Itzikowitz S. Implicit-explicit parallel asynchronous solver for PDEs. SIAM J. Sci. Comput. 19:1998;1366-1404.
3. Amitai D., Averbuch A., Israeli M., Itzikowitz S., Turkel E. A survey of asynchronous finite-difference methods for parabolic PDEs on multiprocessors. Appl. Numer. Math. 12:1993;27-45.
4. Bahi J. Asynchronous Runge-Kutta methods for differential-algebraic systems. Adv. Parallel Comput. 11:1996;205-212.
5. Bahi J. Algorithmes parallèles asynchrones pour des systèmes singuliers. C.R. l'Acad. Sci. Sér. 326:1998;1421-1425.
6. Bahi J., Griepentrog E., Miellou J.-C. Parallel treatment of a class of differential-algebraic systems. SIAM J. Numer. Anal. 23:1996;1969-1980.
7. Bahi J., Miellou J.-C., Rhofir K. Asynchronous multisplitting methods for nonlinear fixed point problems. Numer. Algorithms. 15:1997;315-345.
8. Bai Z.-Z., Migallón V., Penadés J., Szyld D.B. Block and asynchronous two-stage methods for mildly nonlinear systems. Numer. Math. 82:1999;1-20.
9. Barán B., Kaszkurewicz E., Bhaya A. Parallel asynchronous team algorithms: Convergence and performance analysis. IEEE Trans. Parallel Distributed Systems. 7:1996;677-688.
10. Baudet G.M. Asynchronous iterative methods for multiprocessors. J. Assoc. Comput. Mach. 25:1978;226-244.
11. A. Berman, R.J. Plemmons, Nonnegative Matrices in the Mathematical Sciences, Academic Press, New York, Third edition, 1979 (reprinted by SIAM, Philadelphia, 1994).
12. Bertsekas D.P. Distributed asynchronous computation of fixed points. Math. Programming. 27:1983;107-120.
13. Bertsekas D.P., Tsitsiklis J.N. Parallel and Distributed Computation. 1989;Prentice-Hall, Englewood Cliffs, NJ.
14. Bertsekas D.P., Tsitsiklis J.N. Some aspects of parallel and distributed iterative algorithms - a survey. Automatica. 27:1991;3-21.
15. Blathras K., Szyld D.B., Shi Y. Timing models and local stopping criteria for asynchronous iterative algorithms. J. Parallel Distributed Comput. 58:1999;446-465.
16. Bojańczyk A. Optimal asynchronous Newton method for the solution of nonlinear equations. J. Assoc. Comput. Mach. 31:1984;792-803.
17. Bru R., Migallón V., Penadés J., Szyld D.B. Parallel, synchronous and asynchronous two-stage multisplitting methods. Electron. Trans. Numer. Anal. 3:1995;24-38.
18. P. Buchholz, M. Fischer, P. Kemper, Distributed steady state analysis using Kronecker algebra, in: B. Plateau, W.J. Stewart (Eds.), Numerical Solution of Markov Chains (NSMC '99), Prensas Universitarias de Zaragoza, 1999, pp. 76-95.
19. Burrage K. Sequential and Parallel Methods for Ordinary Differential Equations. 1995;Oxford University Press, Oxford.
20. Castel M.J., Migallón V., Penadés J. Convergence of non-stationary multisplitting methods for Hermitian positive definite matrices. Math. Comput. 67:1998;209-220.
21. Chazan D., Miranker W. Chaotic relaxation. Linear Algebra Appl. 2:1969;199-222.
22. Cosnard M., Fraigniaud P. Asynchronous Durand-Kerner and Aberth polynomial root finding methods on a distributed memory multicomputer. Evans D., Joubert G., Peters F. Parallel Computing 89. 1990;North-Holland, Amsterdam.
23. Durand E. Solutions numériques des équations algébriques, Vol. I. 1960;Masson, Paris.
24. El Baz D. A method of terminating asynchronous iterative algorithms on message passing systems. Parallel Algorithms Appl. 9:1996;153-158.
25. El Baz D., Gazen D., Miellou J.-C., Spiteri P. Mise en œuvre de méthodes itératives asynchrones avec communication flexible, application à la résolution d'une classe de problèmes d'optimisation. Calculateurs Parallèles. 8:1996;393-410.
26. El Baz D., Spiteri P., Miellou J.-C. Distributed asynchronous iterative methods with order intervals for a class of nonlinear optimization problems. J. Parallel Distributed Comput. 38:1996;1-15.
27. El Tarazi M.N. Some convergence results for asynchronous algorithms. Numer. Math. 39:1982;325-340.
28. Elsner L., Koltracht I., Neumann M. On the convergence of asynchronous paracontractions with application to tomographic reconstruction from incomplete data. Linear Algebra Appl. 130:1990;65-82.
29. Elsner L., Koltracht I., Neumann M. Convergence of sequential and asynchronous nonlinear paracontractions. Numer. Math. 62:1992;305-319.
30. Frommer A. Generalized nonlinear diagonal dominance and applications to asynchronous iterative methods. J. Comput. Appl. Math. 38:1991;105-124.
31. Frommer A. On asynchronous iterations in partially ordered spaces. Numer. Functional Anal. Optim. 12:1991;315-325.
32. Frommer A. Asynchronous iterations for enclosing solutions of fixed point problems. Atanassova L., Herzberger J. Computer Arithmetic and Enclosure Methods. 1992;243-252 Elsevier, Amsterdam.
33. A. Frommer, Parallele asynchrone Iterationen. in: J. Herzberger (Ed.), Wissenschaftliches Rechnen, Akademie, Berlin, 1995, pp. 187-231 (Chapter 4).
34. Frommer A., Schwandt H. Asynchronous parallel methods for enclosing solutions of nonlinear equations. J. Comput. Appl. Math. 60:1995;47-62.
35. Frommer A., Schwandt H., Szyld D.B. Asynchronous weighted additive Schwarz methods. Electron. Trans. Numer. Anal. 5:1997;48-61.
36. Frommer A., Szyld D.B. H -splittings and two-stage iterative methods Numer. Math. 63:1992;345-356.
37. Frommer A., Szyld D.B. Asynchronous two-stage iterative methods. Numer. Math. 69:1994;141-153.
38. Frommer A., Szyld D.B. Asynchronous iterations with flexible communication for linear systems. Calculateurs Parallèles. 10:1998;421-429.
39. Giraud L., Spitéri P. Résolution parallèle de problèmes aux limites non lineaires. Math. Modelling Numer. Anal. 25:1991;579-606.
40. W. Lioen, J. de Swart, W. van der Veen, Test set for IVP solvers. CWI Amsterdam, Online at http://www.cwi.nl/cwi/projects/IVPtestset .
41. Lubachevsky B., Mitra D. A chaotic asynchronous algorithm for computing the fixed point of a nonnegative matrix of unit spectral radius. J. Assoc. Comput. Mach. 33:1986;130-150.
42. S. Martin, Parallele asynchrone Waveform-Relaxation für Anfangswertaufgaben, Master's thesis, Department of Mathematics, University of Wuppertal, 1999.
43. Miellou J.C. Itérations chaotiques à retards; études de la convergence dans le cas d'espaces partiellement ordonnés. C.R. l'Acad. Sci. Paris, Sér. A. 280:1975;233-236.
44. Miellou J.C., El Baz D., Spitéri P. A new class of asynchronous iterative algorithms with order intervals. Math. Comput. 67:1998;237-255.
45. Mitra D. Asynchronous relaxations for the numerical solution of differential equations by parallel processors. SIAM J. Sci. Statist. Comput. 8:1987;s43-s58.
46. Moré J.J. Nonlinear generalizations of matrix diagonal dominance with application to Gauss-Seidel iterations. SIAM J. Numer. Anal. 9:1972;357-378.
47. Ortega J.M., Rheinboldt W.C. Iterative Solution of Nonlinear Equations in Several Variables. 1970;Academic Press, New York and London.
48. Pereyra V. Asynchronous distributed solution of large scale nonlinear inversion problems. Appl. Numer. Math. 30:1999;31-40.
49. Polman B. Incomplete blockwise factorization of (block). H -matrices Linear Algebra Appl. 90:1987;119-132.
50. Pott M. On the convergence of asynchronous iteration methods for nonlinear paracontractions and consistent linear systems. Linear Algebra Appl. 283:1998;1-33.
51. Savari S.A., Bertserkas D.P. Finite termination of asynchronous iterative algorithms. Parallel Comput. 22:1996;39-56.
52. Shangmeng W., Xiaomei L. A class of stable difference schemes for linear elliptic PDE's and their asynchronous parallel computation. Wuhan Univ. J. Nat. Sci. 1:1996;553-556.
53. Šilc J., Robič B., Ungerer T. Asynchrony in parallel computing: From dataflow to multithreading. Parallel Distributed Comput. Practices. 1:1998;3-30.
54. Strikwerda J.C. A convergence theorem for chaotic asynchronous relaxation. Linear Algebra Appl. 253:1997;15-24.
55. Y. Su, A. Bhaya, Convergence of pseudocontractions and applications to two-stage and asynchronous multisplittings, Technical Report SB97 / NACAD / 05, Laboratory for High Performance Computing, Graduate School of Engineering, Federal University of Rio de Janeiro, 1997.
56. Su Y., Bhaya A., Kaszkurewicz E., Kozyakin V.S. Further results on convergence of asynchronous linear iterations. Linear Algebra Appl. 281:1998;11-24.
57. Szyld D.B. Different models of parallel asynchronous iterations with overlapping blocks. Comput. Appl. Math. 17:1998;101-115.
58. X.-C. Tai, P. Tseng, An asynchronous space decomposition method, in: C.-H. Lai, P.E. Bj ø rstad, M. Cross, O.B. Widlund (Eds.), Eleventh International Conference on Domain Decomposition Methods (London), DDM.org Press, 1999, pp. 348-358.
59. Tseng P. On the rate of convergence of a partially asynchronous gradient projection algorithm. SIAM J. Optim. 1:1991;603-619.
60. Tseng P., Bertsekas D.P., Tsitsiklis J.N. Partially asynchronous, parallel algorithm for network flow and other problems. SIAM J. Control Optim. 28:1990;678-710.
61. Üresin A., Dubois M. Sufficient conditions for the convergence of asynchronous iterations. Parallel Comput. 10:1989;83-92.
62. Varga R.S. On recurring theorems on diagonal dominance. Linear Algebra Appl. 13:1976;1-9.
63. White J., Sangiovanni-Vincentelli A. Relaxation Techniques for the Simulation on VLSI Circuits. 1987;Kluwer Academic Publishers, Boston.
64. Xu J.-J. Convergence of partially asynchronous block quasi-Newton methods for nonlinear systems of equations. J. Comput. Appl. Math. 103:1999;307-321.
65. Aral J., Migallón V., Penadés J. Non-stationary parallel multisplitting algorithms for almost linear systems. Numer. Linear Algebra Appl. 6:1999;79-92.
66. Bru R., Elsner L., Neumann M. Models of parallel chaotic iteration methods. Linear Algebra Appl. 103:1988;175-192.
67. Bru R., Elsner L., Neumann M. Convergence of infinite products of matrices and inner-outer iteration schemes. Electron. Trans. Numer. Anal. 2:1994;183-193.
68. El Baz D. M -functions and parallel asynchronous algorithms SIAM J. Numer. Anal. 27:1990;136-140.