Parallel algorithms for nonlinear problems
SIAM Journal on Algebraic and Discrete Methods
On the stability of the incomplete LU-factorizations and characterizations of H-matrices
Numerische Mathematik
Using MPI: portable parallel programming with the message-passing interface
Using MPI: portable parallel programming with the message-passing interface
Non-stationary Parallel Newton Iterative Methods for Nonlinear Problems
VECPAR '00 Selected Papers and Invited Talks from the 4th International Conference on Vector and Parallel Processing
Iterative Methods for Sparse Linear Systems
Iterative Methods for Sparse Linear Systems
Parallel nonlinear preconditioners on multicore architectures
The Journal of Supercomputing
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Parallel iterative algorithms based on the Newton method and on two of its variations, the Shamanskii method and the Chord method, for solving nonlinear systems are proposed. These algorithms also use techniques from the non–stationary multisplitting methods. Concretely, in order to construct the multisplitting, ILU factorizations are considered. Convergence properties of these parallel methods are studied for H–matrices. Computational results, on a distributed multiprocessor IBM RS/6000 SP, that show the effectiveness of these methods are included to illustrate the theoretical results. Topics: Numerical methods (nonlinear algebra), Parallel and distributed computing.