Parallel algorithms for nonlinear problems
SIAM Journal on Algebraic and Discrete Methods
Iterative solution of nonlinear equations in several variables
Iterative solution of nonlinear equations in several variables
Synchronous and Asynchronous Parallel Algorithms with Overlap for Almost Linear Systems
VECPAR '98 Selected Papers and Invited Talks from the Third International Conference on Vector and Parallel Processing
IPDPS '05 Proceedings of the 19th IEEE International Parallel and Distributed Processing Symposium (IPDPS'05) - Workshop 13 - Volume 14
Asynchronous iterative algorithms for computational science on the grid: three case studies
VECPAR'04 Proceedings of the 6th international conference on High Performance Computing for Computational Science
VECPAR'04 Proceedings of the 6th international conference on High Performance Computing for Computational Science
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Parallel algorithms for solving nonlinear systems are studied. Non-stationary parallel algorithms based on the Newton method are considered. Convergence properties of these methods are studied when the matrix in question is either monotone or an H-matrix. In order to illustrate the behavior of these methods, we implemented these algorithms on two distributed memory multiprocessors. The first platform is an Ethernet network of five 120 MHz Pentiums. The second platform is an IBM RS/6000 with 8 nodes. Several versions of these algorithms are tested. Experiments show that these algorithms can solve the nonlinear system in substantially less time that the current (stationary or non-stationary) parallel nonlinear algorithms based on the multisplitting technique.