# 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} }

- Published 2006
DOI:10.1007/s10665-006-9087-5

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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