Uniform B-spline approximation in Sobolev spaces (Q1370335)

The author presents a new method for approximating functions by uniform B-splines, which is based on the orthogonality relations for those splines in weighted Sobolev spaces. The approximating spline only depends on the local shape of the given function, and the approximation order is optimal. The solution of a constrained approximation problem is simply obtained by first solving the unconstrained problem and then projecting the control points on the feasible set. Furthermore, the approximation scheme is applied to the problems of knot removal and degree reduction.