Parallel Newton methods for sparse systems of nonlinear equations. (English) Zbl 0930.65058
Maugeri, A. (ed.) et al., The proceedings of the workshop “Numerical methods in optimization”, Cortona, Arezzo, Italy, June 9–12, 1997. Palermo: Circolo Matemàtico di Palermo, Suppl. Rend. Circ. Mat. Palermo, II. Ser. 58, 247-257 (1999).
Summary: 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 with \(n=l\times l\) grid with \(l\) up to 64. The results are obtained on the CRAY T3E installed at CINECA (Bologna, Italy) with 32 nodes. The Fortran code runs under MPI implementation.
For the entire collection see [Zbl 0914.00077].
For the entire collection see [Zbl 0914.00077].
MSC:
| 65H10 | Numerical computation of solutions to systems of equations |
| 65Y05 | Parallel numerical computation |
