GENERALIZED NEWTON METHOD FOR NON-CONTINUOUS ONE-VARIABLE EQUATIONS
Corresponding Author(s) : Pham Quy Muoi
UED Journal of Social Sciences, Humanities and Education,
Vol. 7 No. 3 (2017): UED JOURNAL OF SOCIAL SCIENCES, HUMANITIES AND EDUCATION
In this article, we put forward a generalized Newton method to find out the root of a non-continuous equation. Here we only present this method for discontinuous equations in a one-way space. First of all, we propose approximate semi-smooth functions for corresponding non-smooth functions. Then, we prove some basic properties that are necessary for the testification of the convergence of the generalized Newton method. After that, we prove the convergence of this method in non-continuous equations under study. Finally, we present the root findings for a number of specific examples. The numerical examples show that the convergence speed of the generalized Newton method is as fast as that of the traditional Newton method.
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