The exponential accuracy of Fourier and Chebyshev differencing methods. (English) Zbl 0613.65017

Tadmor, Eitan

SIAM J. Numer. Anal. 23, 1-10 (1986).

The author proves that for analytic functions the asymptotic decay rate of the error with either the Fourier or Chebyshev differencing is exponential.

Reviewer: P.Narain

MSC:

65D25	Numerical differentiation
42A20	Convergence and absolute convergence of Fourier and trigonometric series
33C45	Orthogonal polynomials and functions of hypergeometric type (Jacobi, Laguerre, Hermite, Askey scheme, etc.)
65B99	Acceleration of convergence in numerical analysis

Keywords:

Fourier approximation; Chebyshev approximation; pseudospectral differencing; exponential decay