KANTOROVICH-OSTROWSKI CONVERGENCE THEOREMS AND OPTIMAL ERROR-BOUNDS FOR JARRATTS ITERATIVE METHOD

In the first part of this paper, we consider the Kantorovich-Ostrowski convergence theorem of a fourth order method which requires two evaluations of f and one of f for solving nonlinear equations. The convergence of the iteration is established under the following assumptions: Let [formula omitted] be C4 on D with [formula omitted] be a convex open domain [formula omitted] and [formula omitted] for all x,y∊D. Assume that [formula omitted] Here xn and yn are generated by the following schemes: [formula omitted] In the second part, we show that in fact Jarratt's method is equivalent to Newton's method under optimal operator. Also we give an exact error constant and show that it cannot be improved. © 1990, Taylor & Francis Group, LLC. All rights reserved.