Consistent approximations in Newton-type decomposition methods (Q799346)

A class of superlinearly convergent Newton-type decomposition methods for solving structured large systems of nonlinear equations recently introduced by the first two authors [Newton-type decomposition methods for equations arising in Network Analysis Z. Angew. Math. Mech. 64, 397- 405 (1984)] is extended in such a way that consistent approximations to the appearing partial and directional derivatives are permitted. As a concrete realization appropriate directional difference quotients are recommended, which reduce the required number of function evaluations and arithmetical operations considerably. Based on suitable consistency conditions, for a general model algorithm local convergence is established with an R-order \(\lambda >1\) depending on the choice of discretization parameters. The paper concludes with an illustrating numerical example.