| Title |
A New Method of Finding Real Roots of Nonlinear System Using Extended Fixed Point Iterations |
| Authors |
김성수(Sung-Soo Kim) ; 김지수(Ji-Soo Kim) |
| DOI |
http://doi.org/10.5370/KIEE.2018.67.2.277 |
| Keywords |
Geometrical property of an inverse function ; Conventional Fixed Point Iteration Methods ; Extended Fixed Point Iteration Methods ; Polynomial Roots |
| Abstract |
In this paper, a new numerical method of finding the roots of a nonlinear system is proposed, which extends the conventional fixed point iterative method by relaxing the constraints on it. The proposed method determines the real valued roots and expands the convergence region by relaxing the constraints on the conventional fixed point iterative method, which transforms the diverging root searching iterations into the converging iterations by employing the metric induced by the geometrical characteristics of a polynomial. A metric is set to measure the distance between a point of a real-valued function and its corresponding image point of its inverse function. The proposed scheme provides the convenience in finding not only the real roots of polynomials but also the roots of the nonlinear systems in the various application areas of science and engineering. |