The Approximations of Functions and Adaptive Grids

I. G. Burova, E. F. Muzafarova, D. E. Zhilin

Research outputpeer-review

Abstract

A visualization of real function of two variables is often technically difficult. Visualization of complex-valued functions can be simplified by visualizing the real and imaginary parts of these functions. To approximate fast-growing or decreasing functions, often a uniform grid of nodes is not enough and it is necessary to use a special adaptive grid. Therefore, constructing an adaptive mesh of nodes that takes into account the behavior of the function of several variables is of considerable interest. In this paper, we propose one method for constructing an adaptive grid of nodes on a line. Such an adaptive grid can be used to approximate the functions of several variables. Formulae for constructing the adaptive grid of nodes and the results of numerical experiments are given. An approximation of real functions of one and two variables and complex-valued functions is constructed using polynomial and non-polynomial local splines of one variable. Approximations in a rectangular region in the plane are constructed using the tensor product. Formulae for approximations of real and complex-valued functions and examples of visualization of some functions are given.

Original languageEnglish
Title of host publicationProceedings - 2018 International Conference on Applied Mathematics and Computational Science, ICAMCS.NET 2018
PublisherInstitute of Electrical and Electronics Engineers Inc.
Pages171-177
Number of pages7
ISBN (Electronic)9781538694688
DOIs
Publication statusPublished - Oct 2018
Event2018 International Conference on Applied Mathematics and Computational Science, ICAMCS.NET 2018 - Budapest
Duration: 6 Oct 20188 Oct 2018

Publication series

NameProceedings - 2018 International Conference on Applied Mathematics and Computational Science, ICAMCS.NET 2018

Conference

Conference2018 International Conference on Applied Mathematics and Computational Science, ICAMCS.NET 2018
CountryHungary
CityBudapest
Period6/10/188/10/18

Scopus subject areas

  • Computer Science Applications
  • Applied Mathematics
  • Computational Mathematics
  • Control and Optimization
  • Modelling and Simulation

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  • Cite this

    Burova, I. G., Muzafarova, E. F., & Zhilin, D. E. (2018). The Approximations of Functions and Adaptive Grids. In Proceedings - 2018 International Conference on Applied Mathematics and Computational Science, ICAMCS.NET 2018 (pp. 171-177). [8955766] (Proceedings - 2018 International Conference on Applied Mathematics and Computational Science, ICAMCS.NET 2018). Institute of Electrical and Electronics Engineers Inc.. https://doi.org/10.1109/ICAMCS.NET46018.2018.00036