Uniform Approximation of Functions of Two Variables

Abstract

We propose an algorithm to construct a uniform approximation of functions of two variables as a boundary approximation in norm Lp as p → ∞. It is based on root mean square approximation with variable weight function. We propose a technique of successive adjustment of weight function and give examples of uniform approximation of tabulated functions of two variables with the use of the least squares method with variable weight function.

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Correspondence to P. S. Malachivskyy.

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Translated from Kibernetika i Sistemnyi Analiz, No. 3, May–June, 2017, pp. 111–116.

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Malachivskyy, P.S., Matviychuk, Y.N., Pizyur, Y.V. et al. Uniform Approximation of Functions of Two Variables. Cybern Syst Anal 53, 426–431 (2017). https://doi.org/10.1007/s10559-017-9943-5

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Keywords

  • uniform approximation
  • function of two variables
  • approximation in the norm of space L p
  • least squares method with variable weight function