Computing the zeros, maxima and inflection points of Chebyshev, Legendre and Fourier series: solving transcendental equations by spectral interpolation and polynomial rootfinding

@article{Boyd2006ComputingTZ,
  title={Computing the zeros, maxima and inflection points of Chebyshev, Legendre and Fourier series: solving transcendental equations by spectral interpolation and polynomial rootfinding},
  author={John P. Boyd},
  journal={Journal of Engineering Mathematics},
  year={2006},
  volume={56},
  pages={203-219}
}
Recently, both companion-matrix methods and subdivision algorithms have been developed for finding the zeros of a truncated spectral series. Since the Chebyshev or Legendre coefficients of derivatives of a function f(x) can be computed by trivial recurrences from those of the function itself, it follows that finding the maxima, minima and inflection points of a truncated Chebyshev or Fourier series fN(x) is also a problem of finding the zeros of a polynomial when written in truncated Chebyshev… CONTINUE READING
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