Asynchronous multisplitting methods for nonlinear fixed point problems

作者: J. Bahi , J.C. Miellou , K. Rhofir

DOI: 10.1023/A:1019158207224

关键词: Applied mathematicsAsynchronous communicationAlgebra over a fieldMathematicsAsynchronous algorithmsFixed pointNumerical analysisNonlinear systemTheory of computationMathematical optimizationConvergence (routing)

摘要: Our aim is to present for nonlinear problems asynchronous multisplitting algorithms including both the basic situation of O'Leary and White discrete analogue Schwarz's alternating method its multisubdomain extensions moreover their two-stage counterparts. The analysis these methods based on El Tarazi’s convergence theorem iterations leads a good level asynchronism in each considered situations.

参考文章(21)
J. C. Miellou, Algorithmes de relaxation chaotique à retards Revue française d'automatique, informatique, recherche opérationnelle. Analyse numérique. ,vol. 9, pp. 55- 82 ,(1975) , 10.1051/M2AN/197509R100551
Daniel B. Szyld, Violeta Migallón, José Penadés, Rafael Bru, PARALLEL, SYNCHRONOUS AND ASYNCHRONOUS TWO-STAGE MULTISPLITTING METHODS ETNA. Electronic Transactions on Numerical Analysis [electronic only]. ,vol. 3, pp. 24- 38 ,(1995)
Robert J. Plemmons, Abraham Berman, Nonnegative Matrices in the Mathematical Sciences ,(1979)
Bartholomäus Johannes Pohl, A. Frommer, A comparison result for multisplittings based on overlapping blocks and its application to waveform relaxation methods Research report / Seminar für Angewandte Mathematik. ,vol. 1993, ,(1993) , 10.3929/ETHZ-A-004283998
Daniel B. Szyld, Mark T. Jones, Two-stage and multisplitting methods for the parallel solution of linear systems SIAM Journal on Matrix Analysis and Applications. ,vol. 13, pp. 671- 679 ,(1992) , 10.1137/0613042
Dianne P. O’Leary, R. E. White, Multi-Splittings of Matrices and Parallel Solution of Linear Systems Siam Journal on Algebraic and Discrete Methods. ,vol. 6, pp. 630- 640 ,(1985) , 10.1137/0606062
Rafael Bru, Ludwig Elsner, Michael Neumann, Models of parallel chaotic iteration methods Linear Algebra and its Applications. ,vol. 103, pp. 175- 192 ,(1988) , 10.1016/0024-3795(88)90227-3
Andreas Frommer, Daniel B. Szyld, Asynchronous two-stage iterative methods Numerische Mathematik. ,vol. 69, pp. 141- 153 ,(1994) , 10.1007/S002110050085
Andreas Frommer, Bert Pohl, A comparison result for multisplittings and waveform relaxation methods Numerical Linear Algebra With Applications. ,vol. 2, pp. 335- 346 ,(1995) , 10.1002/NLA.1680020403
Mark T. Jones, Daniel B. Szyld, Two-Stage Multisplitting Methods With Overlapping Blocks Numerical Linear Algebra With Applications. ,vol. 3, pp. 113- 124 ,(1994) , 10.1002/(SICI)1099-1506(199603/04)3:2<113::AID-NLA71>3.0.CO;2-G