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

Cesar Martinez-Garza

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.


Full Text: PDF DOI: 10.5539/jmr.v2n3p63

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

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