Generalized Quasilinearization versus Newton's Method for Convex-Concave Functions

Cesar Martinez-Garza


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.

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Journal of Mathematics Research   ISSN 1916-9795 (Print)   ISSN 1916-9809 (Online)

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