On polynomial approximation in the uniform norm by the discrete least squares method

The discrete least squares method is convenient for computing polynomial approximations to functions. We investigate the possibility of using this method to obtain polynomial approximants good in the uniform norm, and find that for a given set ofm nodes, the degreen of the approximating polynomial should be selected so that there is a subset ofn+1 nodes which are close ton+1 Fejér points for the curve. Numerical examples are presented.Sponsored by the United States Army under Contract No. DAAG29-80-C-0041.