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<p>The authors propose a method for constructing the Chebyshev approximation with relative error by a rational expression in a fixed power. It aims to build an intermediate Chebyshev approximation of the values of the root of this power of the approximated function with relative error. The approximation by the rational expression is computed 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 fast convergence of the method for constructing the Chebyshev approximation by the power of a rational expression.</p>

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Chebyshev Approximation by the Power of a Rational Expression

  • 期刊论文

  • 发表日期：

    2025年5月31日

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

摘要

The authors propose a method for constructing the Chebyshev approximation with relative error by a rational expression in a fixed power. It aims to build an intermediate Chebyshev approximation of the values of the root of this power of the approximated function with relative error. The approximation by the rational expression is computed 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 fast convergence of the method for constructing the Chebyshev approximation by the power of a rational expression.