Abstract
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.
This research was supported by Spanish DGESIC grant number PB98-0977.
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Arnal, J., Migallón, V., Penadés, J. (2001). Non-stationary Parallel Newton Iterative Methods for Nonlinear Problems. In: Palma, J.M.L.M., Dongarra, J., Hernández, V. (eds) Vector and Parallel Processing — VECPAR 2000. VECPAR 2000. Lecture Notes in Computer Science, vol 1981. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-44942-6_31
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DOI: https://doi.org/10.1007/3-540-44942-6_31
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