BARYCENTRIC FORMULAS FOR INTERPOLATING TRIGONOMETRIC POLYNOMIALS AND THEIR CONJUGATES

The trigonometric polynomial of minimum degree assuming at the points φk := 2 πk/n (k=0, 1, ..., n-1) given values fk is for n even and φ ≠φk represented by {Mathematical expression} Similar formulas hold for n odd, and for the conjugate polynomial t*(φ{symbol}). A simple recursive algorithm exists for n=2l. This method of evaluating t or t* is numerically stable even for every large n, and for values of φ{symbol} arbitrarily close to some φk. Inasmuch as the evaluation of (*) requires a mere O(n) operations, our formulas are more advantageous than the Fast Fourier Transform if t or t* is to be evaluated only for a small number of values of φ{symbol}. © 1979 Springer-Verlag.