Truncated block Newton and quasi-Newton methods for sparse systems of nonlinear equations. Experiments on parallel platforms

In this paper we give the results found in solving consistent sparse systems of nonlinear equations by an inexact Newton and Quasi-Newton method both combined with a block iterative row-projection linear solver of Cimmino-type. A simple partitioning of the Jacobian matrix was used for solving two nonlinear test problems, that is a tridiagonal problem of size n = 131072 and a nonlinear Poisson problem. The results are obtained on the CRAY T3E installed at CINECA (Bologna, Italy) with 32 nodes. The Fortran code runs under MPI implementation.