The local convergence of ABS methods for nonlinear algebraic equations
The class of algorithms for linear systems recently proposed by the first author, \textit{C. Broyden} and the third author [ibid. 45, 361-376 (1984; Zbl 0535.65009)] is extended to nonlinear algebraic systems. The extended class contains as special cases the algorithms of Brown, Brent and the class proposed by Gay. The local convergence properties are analyzed showing that, under the usual assumptions on the function and mild assumptions on the free parameters, the algorithms are locally convergent with a superlinear Q-rate of convergence (usually quadratic) per major iteration, which is computationally equivalent to a Newton step.
scientific article; zbMATH DE number 3986544
scientific article