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.
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- DOI:10.5539/jmr.v2n3p63
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