Third-Order Newton-Type Methods Combined with Vector Extrapolation for Solving Nonlinear Systems

Abstract EN

We present a third-order method for solving the systems of nonlinear equations.

This method is a Newton-type scheme with the vector extrapolation.

We establish the local and semilocal convergence of this method.

Numerical results show that the composite method is more robust and efficient than a number of Newton-type methods with the other vector extrapolations.