Abstract
Bernoulli polynomials and the related Bernoulli functions are of basic importance in theoretical numerical analysis. It was shown by Golomb and others that the periodic Bernoulli functions serve to construct periodic polynomial splines on uniform meshes. In an unknown paper Wegener investigated remainder formulas for polynomial Lagrange interpolation via Bernoulli functions. We will use Wegener's kernel function to construct periodicB-splines. For uniform meshes we will show that Locher's method of interpolation by translation is applicable to periodicB-splines. This yields an easy and stable algorithm for computing periodic polynomial interpolating splines of arbitrary degree on uniform meshes via discrete Fourier transform.
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