A new method for solving nonlinear systems of equations that is based on functional iterations

Abstract

Regarding solving nonlinear equations systems, there is a main problem that is the number and complexity of the linear algebra operations, and the functional evaluations of the applied algorithm. In this paper, an alternative solution will be proposed by means of constructing a converse of the Banach Theorem fixed-point, only to ℝ2 and ℝ3, in the following sense, this being: each root of a non-linear equations system has been considered as a fixed-point. Besides, the compact set and the continuous functions that fulfil the Banach Theorem are built under certain conditions, those that must satisfy the systemfunctions. Thus each iteration only requires the evaluation of two or three functions.

Keywords

• Nonlinear systems
• fixed point iterations
• zeros
• algorithms
• 02.60.Cb
• 02.60.Pn