Accelerated methods of order \(2p\) for systems of nonlinear equations
Applying the midpoint iteration method to the Newton method for solving the nonsingluar nonlinear problem \(F(x)=0\) with a smooth function \(F: D\subset {\mathbb R}^n\to {\mathbb R}^n\), the authors show that this new method has a convergence order of 5. They also consider approximations of the Jacobian matrix to reduce the computational work and use a few examples to illustrate the convergent orders of the proposed methods. It would be interesting to see a comparison of this method with a 2-step Newton and midpoint methods.
scientific article; zbMATH DE number 5669208
scientific article