We derive a three-term recurrence relation for computing the polynomial of best approximation in the uniform norm to x−1 on a finite interval with positive endpoints. As application, we consider two-level methods for scalar elliptic partial differential equation (PDE), where the relaxation on the fine grid uses the aforementioned polynomial of best approximation. Based on a new smoothing proper...

In this paper, the problem of best uniform polynomial approximation to a continuous function on a compact set X is approached through the partitioning of X and the definition of norms corresponding to the partition and each of the standard Lp norms 1 g p < oo. For computational convenience, a pseudo norm is defined corresponding to each partition. When the partition is chosen appropriately, the...