Automatic Iterative Methods for the Multivariate Solution of Nonlinear Algebraic Equations

Most real world systems express themselves formally as a set of nonlinear algebraic equations. As applications grow, the size and complexity of these equations also increase. In this work, we highlight the key concepts in using the homotopy analysis method as a methodology used to construct efficient iteration formulas for nonlinear equations solving. The proposed method is experimentally characterized according to a set of determined parameters which affect the systems. The experimental results show the potential and limitations of the new method and imply directions for future work.

Authors:

• Rafat Alshorman
• Safwan Al-Shara'
• I. Obeidat

Keywords:

• Nonlinear Algebraic Equations
• Iterative Methods
• Homotopy Analysis Method.

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