A unified approach for solving equations. II: On finite-dimensional spaces (Q2702477)

The author provides a unified approach towards local approximation of solutions of nonlinear operator equations of the form \(F(x)+ Q(x)= 0\), where \(F(\cdot)\) is Fréchet differentiable and \(Q(\cdot)\) is continuous. The (unknown) Fréchet derivative of \(F(\cdot)\) is replaced by a linear operator, which is an approximation of the exact derivative. In the first part of the paper [ibid. 201-254 (2000; reviewed above)], the mesh independence principle is generalized to include perturbed Newton-like methods. In the second part the results are applied to non-exact Newton-like methods. Convergence is proved and truncation error analysis is presented. Applications to integral equations and two-point boundary value problems for ordinary and partial differential equations are indicated.NEWLINENEWLINEFor the entire collection see [Zbl 0954.65001].