Abstract

In this paper we use the Method of Generalized Quasilinearization to obtain monotone Newton-like comparative schemes to solve the equation F(x)=0, where  F(x) Î C[W,R].  Here, F(x) admits the decomposition F(x)=f(x)+g(x),  where f(x) and g(x)  are convex and concave functions in W,  respectively.  The monotone sequences of iterates are shown to converge quadratically.  Four cases are explored in this manuscript.

This work is licensed under a Creative Commons Attribution 4.0 License.