ERROR-BOUNDS FOR GAUSS TYPE QUADRATURE-FORMULAS RELATED TO SPACES OF SPLINES WITH EQUIDISTANT KNOTS

Error bounds for the Gauss type quadrature formulae Q(n)(G), Q(n+1)(L) and Q(n+1)(R) (Gauss, Lobatto and Radau formulae) related to the spac es of polynomial spline functions of degree r-1 with equidistant knots are obtained. It is shown that these quadrature rules are asymptotica lly optimal in the Sobolev space W-infinity(r) for all r, and in W-p(r ) (1 less than or equal to p less than or equal to infinity) for odd r . Some inequalities involving the Gaussian nodes and weights are also established. (C) 1995 Academic Press, Inc.