KOCAK'S ACCELERATION METHOD SMOOTHLY GEARS UP ITERATIVE SOLVERS

Year 2014, Volume: 2 Issue: 2, 109 - 119, 01.12.2014

Mehmet Çetin Koçak

Abstract

Consider a scalar repetitive scheme symbolically represented byxk+1= g(xk) where k is the iteration count. Let z and n respectively denote the target fixed-point and convergence order of g. Ko¸cak’s method gKaccelerates g by actually solving a superior secondary solver obtained from afixed-point preserving transformationg where G is a gain and m is the slope of a straight line joining g and g = x= x + G(g − x) = (g − mx)/(1 − m), m = 1 − 1/G, G = 1/(1 − m)

Keywords

Non-linear equations, Iterative methods; Newton’s method; Os65B99, 65H05

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• Tando˘gan, Ankara, Turkey E-mail address: [e-mail]