文章基本信息

标题：Construction of a numerical method for finding the zeros of both smooth and nonsmooth functions
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作者：Roman Bihun ; Gregoriy Tsehelyk
期刊名称：Eastern-European Journal of Enterprise Technologies
印刷版ISSN：1729-3774
电子版ISSN：1729-4061
出版年度：2017
卷号：2
期号：4
页码：58-64
DOI：10.15587/1729-4061.2017.99273
语种：English
出版社：PC Technology Center
摘要：Here we report building a numerical method for finding the zeros of a function of one real variable using the apparatus of nonclassical Newton’s minorants and diagrams of functions', given in the tabular form. The examples of the search for zeros of functions are given.A problem on finding the roots of equations belongs to important problems of applied mathematics. Classical methods of finding the zeroes of functions require first to isolate the roots and then to find them. In order to find a separate root with a given accuracy, it is necessary to choose one of the points in the vicinity that contains the root as the initial approximation and to employ an appropriate iterative process.The numerical method constructed does not require additional information about the location of roots and has many advantages over other methods for finding the zeros of functions, in particular: simplicity and visual representation of the method. Because of this, it can gain a widespread application in many areas, such as physics, mechanics, and natural sciences. By using the method built, it is possible to find the roots in a linear time, which is rather fast. The practical value of a numerical method is largely determined by the speed of obtaining the solution.
关键词：minorant of a function;zero of a function;Chebyshev polynomial;Newton's diagram;smooth and nonsmooth function