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KIAM Preprint № 27, Moscow, 2024
Authors: Varin V.P.
Spectral methods for polynomial interpolation and approximation
Abstract:
Classical problem of interpolation and approximation of functions with polynomials is considered here as a special case of spectral representation of functions. We developed this approach earlier for Legendre and Chebyshev orthogonal polynomials. Here we use Newton's fundamental polynomials as basis functions. We demonstrate that the spectral approach has computational advantages over the divided differences method. In a number of problems, Newton and Hermite interpolations are indistinguishable in our approach and computed by the same formulas. Also, computational algorithms that we constructed earlier with the use of orthogonal polynomials are adapted without modifications for use of Newton and Hermite polynomials.
Keywords:
specral methods, Newton and Hermite polynomials, interpolation and approximation
Publication language: russian,  pages: 20
Research direction:
Mathematical problems and theory of numerical methods
Russian source text:
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About authors:
  • Varin Victor Petrovich,  orcid.org/0000-0001-7324-1823KIAM RAS