Malachivskyy P.S., Pizyur Y.V., Malachivskyi R.P., Ukhanska O.M.
Chebyshev approximation of functions of several variables

The authors propose an algorithm to construct Chebyshev approximation for functions of several variables by a generalized polynomial as a limiting approximation in the norm of space Lp as p → ∞. It is based on serial construction of power-average approximations using the least squares method with variable weight function. The convergence of the method provides an original way to consistently refine the values of the weight function, which takes into account the results of approximation at all previous iterations. The authors describe the methods of calculating the Chebyshev approximation with absolute and relative errors. The results of test examples confirm the efficiency of using the method to obtain Chebyshev approximation of tabular continuous functions of one, two, and three variables. © 2020, Springer Science+Business Media, LLC, part of Springer Nature.

Keywords: Chebyshev (uniform) approximation, functions of several variables, least squares method, power-mean approximation, variable weight function, Approximation algorithms, Chebyshev approximation, Polynomial approximation, Chebyshev, Functions of several variables, Least squares methods, Power means, Variable weight, Least squares approximations

Cite:
Malachivskyy P.S., Pizyur Y.V., Malachivskyi R.P., Ukhanska O.M. (2020). Chebyshev approximation of functions of several variables. Cybernetics and Systems Analysis, 56 (1), 138–146. doi: https://doi.org/10.1007/s10559-020-00227-8 http://jnas.nbuv.gov.ua/article/UJRN-0001074970 [In Ukrainian].