Abstract: | For the Favard class Fr in the space C2π of continuous 2π-periodic functions we solve the following problem. Given x
and knots x0< x1 < ··· < xv−1., xu− 2π we determine weights xki(0 k · n, 0 j < r) such that is minimal. The optimal weights are unique (except for a trivial case) and we obtain them from a system of periodic polynomial splines ukj(0 k < n, 0 j< r): αkj = ukj(x). These splines induce an interpolation operator whose degree of approximation with respect to the class Fr is minimal if the knots are equidistant. Finally, we describe an efficient numerical procedure which shows how to compute the interpolation spline in the equidistant case. |