The Jarratt method in Banach space setting
Convergence and error estimates of the Jarratt iterative method \(y_ n= x_ n- F'(x_ n)^{-1} F(x_ n)\), \[ H(x_ n, y_ n)= F'(x_ n)^{-1} [F'(x_ n+\textstyle{{2\over 3}}(y_ n- x_ n))- F'(x_ n)], \] \(x_{n+1}= y_ n- {3\over 4} [I+ {3\over 2} H(x_ n, y_ n)]^{-1} H(x_ n, y_ n)(y_ n- x_ n)\), are given for solving nonlinear operator equations \(F(x)= 0\). Here \(F\) maps a convex subset of \(X\) into \(Y\) which are Banach spaces. A quadratic integral equation is discussed as an example.
scientific article; zbMATH DE number 641401