کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
4629272 1340576 2013 6 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
Koçak's method shows that an unwittingly exaggerated convergence order is in fact 2
موضوعات مرتبط
مهندسی و علوم پایه ریاضیات ریاضیات کاربردی
پیش نمایش صفحه اول مقاله
Koçak's method shows that an unwittingly exaggerated convergence order is in fact 2
چکیده انگلیسی
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) − x) = (g(x) − m(x)x)/(1 − m(x)) where G(x) = 1/(1 − m(x)) is a gain and m(x) = 1 − 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) − 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.
ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Applied Mathematics and Computation - Volume 219, Issue 19, 1 June 2013, Pages 10053-10058
نویسندگان
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