SOME PROBLEMS ON OPTIMAL QUADRATURE

Abstract

Using the connection between optimal approximation of linear operators and spline interpolation established by I.J. Schoenberg (35), the '-function method of D.V. Ionescu (17), and a more general method given by A. Ghizzetti and A. Ossicini (14), the one-to-one correspondence be- tween the monosplines and quadrature formulas given by I.J. Schoenberg (36, 37), and the minimal norm property of orthogonal polynomials, the authors study optimal quadrature formulas in the sense of Sard (33) and in the sense of Nikolski (27), respectively, with respect to the error criterion. Many examples are given.