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<p>The authors propose a method for constructing the Chebyshev approximation with an absolute error by the logarithm of a rational expression. It intends to build the intermediate Chebyshev approximation with a relative error of the exponent of the approximated function by a rational expression. The approximation by the rational expression is calculated as the boundary of mean-power approximation using an iterative scheme based on the least squares method with two variable weight functions. The results of solving the test examples confirm the fast convergence of the method.</p>

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The Chebyshev Approximation by the Logarithm of a Rational Expression

  • 期刊论文

  • 发表日期：

    2025年1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 with an absolute error by the logarithm of a rational expression. It intends to build the intermediate Chebyshev approximation with a relative error of the exponent of the approximated function by a rational expression. The approximation by the rational expression is calculated as the boundary of mean-power approximation using an iterative scheme based on the least squares method with two variable weight functions. The results of solving the test examples confirm the fast convergence of the method.