Introduction

Of particular interest here is interpolation by polynomials of degree at most n, which has been extensively studied by Reimer [15]. For extremal fundamen­ tal systems, which maximize the determinant of the interpolation matrix (see Section 3), Reimer has shown that the norm ||An| of the interpolation operator, considered as a map from C (§2) to C(§2), is bounded by (n + l)2. Given a set of points for polynomial interpolation, it is then straightforward to use these in a numerical quadrature rule, (see for example Reimer [16] and Fliege and Maier [6]).