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Chebyshev interpolation is a method for approximating a function that is numerically stable and can provide accurate approximations even for highly oscillatory functions. In this study, we focus on numerical implementations of Chebyshev interpolation. In particular, we introduce a method for numerically computing the derivative, rootfinding, computing maxima and minima of a given Chebyshev interpolation function using the Julia language. The main contribution of this study is that our implementation can be rigorously computed based on interval arithmetic.

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Rigorous Numerical Computations with the Chebyshev Interpolation Using the Julia Language

  • 会议论文

  • 发表日期：

    2025年

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  • Shinsuke Kondo,
  • Akitoshi Takayasu

摘要

Chebyshev interpolation is a method for approximating a function that is numerically stable and can provide accurate approximations even for highly oscillatory functions. In this study, we focus on numerical implementations of Chebyshev interpolation. In particular, we introduce a method for numerically computing the derivative, rootfinding, computing maxima and minima of a given Chebyshev interpolation function using the Julia language. The main contribution of this study is that our implementation can be rigorously computed based on interval arithmetic.