KOCAK'S ACCELERATION METHOD SMOOTHLY GEARS UP ITERATIVE SOLVERS

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)