On the solution of undetermined systems of nonlinear equations in Euclidean spaces. (English) Zbl 0809.47053

Summary: We provide sufficient conditions for the convergence of Newton-like methods to a locally unique solution of undetermined systems of linear equations with nondifferentiable terms in an \(m\)-dimensional Euclidean space. We assume that the operators involved and some of their Fréchet- derivatives are bounded in norm by some nondecreasing real functions of two variables. Special choices of these real functions reduce to the usual Lipschitz constants. Our error bounds can then be compared favorably with bounds already in the literature.
The results obtained here can be used to solve systems of nonlinear equations solved by continuation methods, eigenvalues and other problems.


47J25 Iterative procedures involving nonlinear operators
65H10 Numerical computation of solutions to systems of equations