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http://dx.doi.org/10.5370/KIEE.2018.67.2.277

A New Method of Finding Real Roots of Nonlinear System Using Extended Fixed Point Iterations  

Kim, Sung-Soo (Department of Electrical Engineering, Chungbuk National University)
Kim, Ji-Soo (Department of Earth and Environmental Science, Chungbuk National University)
Publication Information
The Transactions of The Korean Institute of Electrical Engineers / v.67, no.2, 2018 , pp. 277-284 More about this Journal
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.
Keywords
Geometrical property of an inverse function; Conventional Fixed Point Iteration Methods; Extended Fixed Point Iteration Methods; Polynomial Roots;
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