Error Bounds for Gauss Type Quadrature Formulas Related to Spaces of Splines with Equidistant Knots Original Research Article

Error bounds for the Gauss type quadrature formulae QGn, QLn+1 and QRn+1 (Gauss, Lobatto and Radau formulae) related to the spaces of polynomial spline functions of degree r−1 with equidistant knots are obtained. It is shown that these quadrature rules are asymptotically optimal in the Sobolev space Wr∞ for all r, and in Wrp (1 ≤ p ≤ ∞) for odd r. Some inequalities involving the Gaussian nodes and weights are also established.