若干中点迭代法的收敛性

The King-Werner iteration xn 1= xn -F‘(1/2(xn yn))^-1 F(xn);yn 1=xn 1-F‘(1/2(xn yn))^-1F(xn 1) which is used for solving the operator eqution in Banach space F(x) = 0 requires the inverse of the opterator‘s derivative.Now in this paper a deformation King-Werner method without use of inverse is presented and the convergence of this method is proved with the skill of the majoring function. In addition, for the existed convergent theorem the convergent condtions are amended. The corresponding convergence theorem holds also with the amended conditions and its error bounds is obtained. At last a midpoint method of order 1 √2 : yn=xn-F‘(xn)^-1F(xn);xn 1=xn-F‘(xn yn/2)^-1F(xn) which is studied by D.Chen and I.K.Argros is convergent withby milder conditions by recurence relations.

THE CONVERGENCES OF SEVERAL MIDPOINT ITERATIVE METHODS

The King-Werner iteration xn+1 = xn - F'(1/2(xn + yn))-1 F(xn);yn+1 = Xn+1 -F'(1/2(xn + yn))-1 F(xn+1) which is used for solving the operator eqution in Banach space F(x) - 0 requires the inverse of the opterator's derivative.Now in this paper a deformation King-Werner method without use of inverse is presented and the convergence of this method is proved with the skill of the majoring function. In addition, for the existed convergent theorem the convergent cond-tions are amended. The corresponding convergence theorem holds also with the amended conditions and its error bounds is obtained. At last a midpoint method of order 1 + 2~(1/2): yn = xn - F'(xn)-1 F(xn);xn+1 = xn - F'(xn+yn/2)-1F(xn) which is studied by D.Chen and I.K.Argros is convergent with milder conditions by recurence relations.