Abstract

Abstract. 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.