Showing papers by "José Mario Martínez published in 1979"
TL;DR: In this article, the authors generalized the methods of Brent and Brown for solving systems of equations without computation of analytic derivatives by exploiting the cases in which a substantial part of the work necessary to evaluate a function is common to the evaluation of another function.
Abstract: We generalize the methods of Brent and Brown for solving systems of equations without computation of analytic derivatives. The generalized methods try to exploit the cases in which a substantial part of the work necessary to evaluate a function is common to the evaluation of another function. Local convergence results and some numerical experience are given.
23 citations
TL;DR: In this article, the authors introduce three new implementations of the sequential secant method for solving nonlinear simultaneous equations and store orthogonal factorizations of some of the matrices involved.
Abstract: We introduce three new implementations of the sequential secant method for solving nonlinear simultaneous equations. Following the ideas of Gragg and Stewart, we store orthogonal factorizations of some of the matrices involved. Degeneracy in the increments of the independent variable is corrected according to simple and theoretically justified procedures. Some numerical experiences are also given.
18 citations