Multi-step nonlinear ABS methods and their efficiency analysis
The multi-step principle developed 20 years ago for Newton's method and most of its discretized versions is applied to nonlinear ABS methods. In the multi-step methods each major iteration step consists of \(m+1\) minor iterations where the derivative information is fixed and only function values are to be computed. The method is shown to converge locally with O-order \(m+2\), and for given dimension n the optimal step number m which minimizes an asymptotic measure of complexity is determined.
scientific article; zbMATH DE number 4203588