Numerical estimation of projection constants

We calculate upper and lower bounds for the minimal norm of projections from continuous functions onto polynomials of a given maximal degree. This is done by a discretization of the basic interval, the calculation of the minimal projection for the discretized problem by the simplex method, and an estimation of the discretization error according to an approach of Motte [3]. Explicit bounds for norms of minimal projections into polynomial spaces up to the degree 10 are tabulated. AMS Subject classification: 41A10 41A35 41A44