Computational & Applied Mathematics
On-line version ISSN 1807-0302
ECHEBEST, N.; SCHUVERDT, M. L. and VIGNAU, R. P.. Two derivative-free methods for solving underdetermined nonlinear systems of equations. Comput. Appl. Math. [online]. 2011, vol.30, n.1, pp. 217-245. ISSN 1807-0302. http://dx.doi.org/10.1590/S1807-03022011000100011.
In this paper, two different approaches to solve underdetermined nonlinear system of equations are proposed. In one of them, the derivative-free method defined by La Cruz, Martínez and Raydan for solving square nonlinear systems is modified and extended to cope with the underdetermined case. The other approach is a Quasi-Newton method that uses the Broyden update formula and the globalized line search that combines the strategy of Grippo, Lampariello and Lucidi with the Li and Fukushima one. Global convergence results for both methods are proved and numerical experiments are presented.
Keywords : underdetermined nonlinear systems; Quasi-Newton method; derivative-free line search; spectral step length; global convergence.