On interpolation variants of Newton's method for functions of several variables
Let \(F:D\subset R^n\to R^n\) be a sufficiently differentiable function. The convergence of the iterative method \[ x^{k+1}=x^k-(\sum_{h=1}^m A_hJ_F(\eta_h(x^k)))^{-1} F(x^k),\quad k\geq 0 \] towards a certain zero of \(F\) is discussed, via generalized Newton methods. Some numerical examples are given so as to illustrate the method.
scientific article; zbMATH DE number 5696562