Chebyshev Approximation of Multivariable Functions by the Exponential Expression

1. R. Cavoretto, “A numerical algorithm for multidimensional modeling of scattered data points,” Comp. Appl. Math., Vol. 34, 65–80 (2015).

   Article  MathSciNet  Google Scholar 

2. A. Iske, Approximation Theory and Algorithms for Data Analysis, Springer, New York (2018).

   Book  Google Scholar 

3. A. A. Kalenchuk-Porkhanova, “Best Chebyshev approximation of functions of one and many variables,” Cybern. Syst. Analysis, Vol. 45, No. 6, 988–996 (2009).

   Article  MathSciNet  Google Scholar 

4. L. Collatz and W. Krabs, Theory of Approximations. Chebyshev Approximations and their Applications [Russian translation], Nauka, Moscow (1978).

5. C. B. Dunham, “Approximation with one (or few) parameters nonlinear,” J. Comp. and Applied Math., Vol. 21, No. 1, 115–118 (1988).

   Article  MathSciNet  Google Scholar 

6. D. Braess, Nonlinear Approximation Theory, Springer-Verlag, Berlin–Heidelberg (1986).

   Book  Google Scholar 

7. R. A. DeVore, “Nonlinear approximation,” Acta Numerica, Cambridge Univ. Press, Vol. 7, 51–150 (1998).

   Google Scholar 

8. R. A. DeVore and A. Kunoth, “Nonlinear approximation and its applications,” in: Multiscale, Nonlinear and Adaptive Approximation, Springer-Verlag, Berlin–Heidelberg (2009), pp. 169–201.

9. V. Temlyakov, “Nonlinear methods of approximation,” J. of FOCM, Vol. 3, 33–107 (2003).

   MathSciNet  MATH  Google Scholar 

10. Y. L. Luke, Special Mathematical Functions and their Approximations, Acad. Press (1975).

    MATH  Google Scholar 

11. B. A. Popov and G. S. Tesler, Computer Calculation of Functions: A Reference Book [in Russian], Naukova Dumka, Kyiv (1984).

    Google Scholar 

12. B. A. Popov and G. S. Tesler, Approximation of Functions for Engineering Applications [in Russian], Naukova Dumka, Kyiv (1980).

    Google Scholar 

13. C. B. Dunham, “Difficulties in fitting scientific data,” ACM SIGNUM Newsletter, Vol. 25, No. 3, 15–20 (1990).

    Article  Google Scholar 

14. A. O. Kalenchuk-Porkhanova and L. P. Vakal, “Recovering functional dependences based on nonlinear approximations of some types,” Abstr. of Intern. Conf. “Problems of decision making under uncertainties,” May 21–25, 2007, Chernivtsi, Ukraine (2007), pp. 135–137.

15. Zuowei Shen, Haizhao Yang, and Shijun Zhang, “Nonlinear approximation via compositions,” Neural Networks, Vol. 119, Nov., 74–84 (2019).

16. P. S. Malachivskyy, Ya. V. Pizyur, N. V. Danchak, and E. B. Orazov, “Chebyshev approximation by exponential-power expression,” Cybern. Syst. Analysis, Vol. 49, No. 6, 877–881 (2013).

    Article  MathSciNet  Google Scholar 

17. P. S. Malachivskyy, Ya. V. Pizyur, N. V. Danchak, and E. B. Orazov, “Chebyshev approximation by exponential expression with relative error,” Cybern. Syst. Analysis, Vol. 51, No. 2, 286–290 (2015).

    Article  MathSciNet  Google Scholar 

18. P. S. Malachivskyy, Y. N. Matviychuk, Ya. V. Pizyur, and R. P. Malachivskyi, “Uniform approximation of functions of two variables,” Cybern. Syst. Analysis, Vol. 53, No. 3, 426–431 (2017).

    Article  MathSciNet  Google Scholar 

19. P. S. Malachivskyy, Ya. V. Pizyur, R. P. Malachivskyi, and O. M. Ukhanska, “Chebyshev approximation of functions of several variables,” Cybern. Syst. Analysis, Vol. 56, No. 1, 76–86 (2020).

    Article  Google Scholar 

20. E. Ya. Remez, Fundamentals of Numerical Methods of Chebyshev Approximation [in Russian], Naukova Dumka Kyiv, (1969).

    Google Scholar 

21. P. S. Malachivskyy and V. V. Skopetsky, Continuous and Smooth Minimax Spline Approximation [in Ukrainian], Naukova Dumka, Kyiv (2013).

    Google Scholar 

22. P. S. Malachivskyy and Ya. V. Pizyur, Solving Problems in the Maple Environment [in Ukrainian], RASTR-7, Lviv (2016).

Download references