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<p>This paper addresses the challenge of function approximation using Hermite interpolation on equally spaced nodes. In this setting, standard polynomial interpolation suffers from the Runge phenomenon. To mitigate this issue, we propose an extension of the constrained mock-Chebyshev least squares approximation technique to Hermite interpolation. This approach leverages both function and derivative evaluations, resulting in more accurate approximations. Numerical experiments are implemented in order to illustrate the effectiveness of the proposed method.</p>

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Constrained mock-Chebyshev least squares approximation for Hermite interpolation

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2025年3月22日

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  • Francesco Dell’Accio,
  • Francisco Marcellán,
  • Federico Nudo

摘要

This paper addresses the challenge of function approximation using Hermite interpolation on equally spaced nodes. In this setting, standard polynomial interpolation suffers from the Runge phenomenon. To mitigate this issue, we propose an extension of the constrained mock-Chebyshev least squares approximation technique to Hermite interpolation. This approach leverages both function and derivative evaluations, resulting in more accurate approximations. Numerical experiments are implemented in order to illustrate the effectiveness of the proposed method.