On a Moser-Steffensen type method for nonlinear systems of equations
For researchers in numerical analysis, this provides a derivative-free method with quadratic convergence, though it is an incremental improvement over existing techniques.
The paper constructs and analyzes a derivative-free iterative method for nonlinear systems that achieves quadratic convergence without evaluating derivatives or inverse operators, improving applicability over Newton and Steffensen methods.
This paper is devoted to the construction and analysis of a Moser-Steffensen iterative scheme. The method has quadratic convergence without evaluating any derivative nor inverse operator. We present a complete study of the order of convergence for systems of equations, hypotheses ensuring the local convergence and finally we focus our attention to its numerical behavior. The conclusion is that the method improves the applicability of both Newton and Steffensen methods having the same order of convergence.