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.
Wen Zhou. Jisheng Kou. "Third-Order Newton-Type Methods Combined with Vector Extrapolation for Solving Nonlinear Systems." Abstr. Appl. Anal. 2014 (SI32) 1 - 8, 2014. https://doi.org/10.1155/2014/601745