KOCAK`S ACCELERATION METHOD SMOOTHLY GEARS UP ITERATIVE SOLVERS

Authors : Mehmet Çetin KOÇAK

Pages : 109-119

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Publication Date : 2014-12-01

Article Type : Research Paper

Abstract :Consider a scalar repetitive scheme symbolically represented byxk+1= ginsert ignore into journalissuearticles values(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 + Ginsert ignore into journalissuearticles values(g − x); = insert ignore into journalissuearticles values(g − mx);/insert ignore into journalissuearticles values(1 − m);, m = 1 − 1/G, G = 1/insert ignore into journalissuearticles values(1 − m);
Keywords : Non linear equations, Iterative methods, Newtons method, Os65B99, 65H05