Construction of a numerical method for finding the zeros of both smooth and nonsmooth functions
DOI:
https://doi.org/10.15587/1729-4061.2017.99273Keywords:
minorant of a function, zero of a function, Chebyshev polynomial, Newton's diagram, smooth and nonsmooth functionAbstract
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.
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