An Algorithm for the Determination of the Polynomial of Best Minimax Approximation to a Function Defined on a Finite Point Set

where q(x) is any polynomial of degree less than or equM to n. Although the properties which determine p ( x ) uniquely are well known, we state them here for future reference. In what follows u = (u0, u l , • -, Un+l) will always denote a vector, the coordinates of which are points of S satisfying uo < u~ < .. • < u~+~. We shall denote the class of such vectors by T. For u in T, consider the following equations: