GMRES: a generalized minimal residual algorithm for solving nonsymmetric linear systems
SIAM Journal on Scientific and Statistical Computing
LAPACK's user's guide
Introduction to parallel computing: design and analysis of algorithms
Introduction to parallel computing: design and analysis of algorithms
Using MPI: portable parallel programming with the message-passing interface
Using MPI: portable parallel programming with the message-passing interface
Matrix computations (3rd ed.)
ScaLAPACK user's guide
Testing Unconstrained Optimization Software
ACM Transactions on Mathematical Software (TOMS)
On the Influence of the Orthogonalization Scheme on the Parallel Performance of GMRES
Euro-Par '98 Proceedings of the 4th International Euro-Par Conference on Parallel Processing
LAPACK Working Note 73: Basic Linear Algebra Communication Subprograms: Analysis and Implementation Across Multiple Parallel Architectures
Three parallel algorithms for solving nonlinear systems and optimization problems
VECPAR'04 Proceedings of the 6th international conference on High Performance Computing for Computational Science
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In this work we describe a portable sequential and parallel algorithm based on Newton's method, for solving nonlinear systems. We used the GMRES iterative method to solve the inner iteration. To control the inner iteration as much as possible and avoid the oversolving problem, we also parallelized several forcing term criterions. We implemented the parallel algorithms using the parallel numerical linear algebra library SCALAPACK based on the MPI environment. Experimental results have been obtained using a cluster of Pentium II PC's connected through a Myrinet network. To test our algorithms we used three different test problems, the H-Chandrasekhar problem, computing the intersection point of several hyper-surfaces, and the Extended Rosenbrock Problem. The latter requires some improvements for the method to work with structured sparse matrices and chaotic techniques. The algorithm obtained shows a good scalability in most cases. This work is included in a framework tool we are developing where, given a problem that implies solving a nonlinear system, the best nonlinear method must be chosen to solve the problem. The method we present here is one of the methods we implemented.