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<p>A method for constructing Chebyshev approximations of multivariable functions by exponential, logarithmic, and power expressions of a generalized polynomial with an interpolation condition is proposed. The method is based on constructing an intermediate Chebyshev approximation by a generalized polynomial with an interpolation condition for an appropriate functional transformation of the approximated function. The approximation by a generalized polynomial is computed as a limiting mean-power approximation by an iterative scheme using the least squares method with a variable weight function. Test examples confirming the rapid convergence of the method are presented.</p>

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Chebyshev Approximation of Multivariable Functions by a Nonlinear Expression of a Generalized Polynomial with a Condition

  • 期刊论文

  • 发表日期：

    2026年7月31日

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  • P. S. Malachivskyy,
  • L. S. Melnychok,
  • O. V. Shevchuk

摘要

A method for constructing Chebyshev approximations of multivariable functions by exponential, logarithmic, and power expressions of a generalized polynomial with an interpolation condition is proposed. The method is based on constructing an intermediate Chebyshev approximation by a generalized polynomial with an interpolation condition for an appropriate functional transformation of the approximated function. The approximation by a generalized polynomial is computed as a limiting mean-power approximation by an iterative scheme using the least squares method with a variable weight function. Test examples confirming the rapid convergence of the method are presented.