Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4629272 | Applied Mathematics and Computation | 2013 | 6 Pages |
Abstract
Iterative solution of a nonlinear equation f(x) = 0 usually means a repetitive scheme to locate a fixed point of a related equation x = g(x). Koçak's acceleration method smoothly gears up iterations with the aid of a superior secondary solver gK = x + G(x)(g(x) â x) = (g(x) â m(x)x)/(1 â m(x)) where G(x) = 1/(1 â m(x)) is a gain and m(x) = 1 â 1/G(x) is a straight line slope. The accelerator shows that a previously published article [A. Biazar, A. Amirtemoori, An improvement to the fixed point iterative method, AMC 182 (2006) 567-571] unwittingly exaggerated the convergence order of the solver it presented. This solver boils down to an indirect application of Newton's method solving g(x) â x = 0 which means that it is of second order. Hence, their claim that it “increases the order of convergence as much as desired” is false! The scheme wastes higher derivatives.
Related Topics
Physical Sciences and Engineering
Mathematics
Applied Mathematics
Authors
Mehmet Ãetin Koçak,