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<p>The authors propose a method for constructing the Chebyshev approximation of multivariable functions using an expression that is an exponent, a logarithm, and a fixed real power of a rational expression. It involves constructing an intermediate Chebyshev approximation by a rational expression of the corresponding functional transformation of the approximated function. The approximation by a rational expression is calculated as a limiting mean-power approximation using an iterative scheme based on the least squares method with two variable weight functions. The authors present test examples to confirm the rapid convergence of the proposed method.</p>

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Chebyshev Approximation of Multivariable Functions by a Nonlinear Function of a Rational Expression

  • 期刊论文

  • 发表日期：

    2025年7月1日

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  • P. S. Malachivskyy,
  • L. S. Melnychok

摘要

The authors propose a method for constructing the Chebyshev approximation of multivariable functions using an expression that is an exponent, a logarithm, and a fixed real power of a rational expression. It involves constructing an intermediate Chebyshev approximation by a rational expression of the corresponding functional transformation of the approximated function. The approximation by a rational expression is calculated as a limiting mean-power approximation using an iterative scheme based on the least squares method with two variable weight functions. The authors present test examples to confirm the rapid convergence of the proposed method.