Iterative method for solving nonlinear singular problems (Q2410880)

A \(p\)-factor method for solving nonlinear equations of the form \(F(x) = 0\), \(F : \mathbb R^{n} \rightarrow \mathbb R^{m}\) in the singular (irregular) case is introduced. The conditions that have to be fulfilled at the initial point \(x_{0}\) to obtain the existence of a solution of the nonlinear equation \(F(x) = 0\) are found. Convergence and convergence rate of the presented \(p\)-factor method are also studied.