Number Of Amendments To The King-werner Iterative Method And Convergence

The algorithm problem of solving the nonlinear operator equationsF(x) = 0in Banach Space has been one of the most interesting problems for many numerical scientists for a long time . At present time one of efficient algorithms to solve this problem is the iterative method. The King-Werner Methodis a efficient one for solving the nonlinear equations.This paper is made up of five sections.In section one,some relevent theorems about The King-Werner Method are interpreted. In section two we derived one iterative method for solving the nonlinear equations,proved the properities of the majoring funtion and the convergence of the majoring sequence,gave one variety of iterative methmod and proved it. Finally , the convergent condtions with one existed convergent theorem are amended and we also prove its convergence and get its error bounds.At last ,it is proved that a midpint mehtod is convenge under the criterion αof weak conditon.