科研之友
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摘要
The interpolating spline or trigonometric polynomial to a function at equally spaced points approximates the Dirichlet partial sums of its Fourier series with accuracy depending only on the neglected coefficients. We show that the Fej,r mean of the Dirichlet sums can be approximated by the arithmetic mean of two Fej,r trigonometric interpolants, one at the points with even indexes and one at the points with odd indexes, with an error depending only on the neglected Fourier coefficients and it is positive for positive functions. We also consider the case of Fej,r spline interpolants and a constructive relation between Hermite and Fej,r interpolants.
- 出版日期2013-9
