Bounds are derived for both the L2- and L∞-norms of the error inapproximating sufficiently smooth functions by polynomial splines using an integral least square technique based on the theory of orthogonal projection in real Hilbert space. Quadrature schemes for the approximate solution of this least square problem are examined and bounds for the error due to the use of such schemes are derived. The question of the consistency of such quadrature schemes with the least square error is investigated and asymptotic results are presented. Numerical results are also included.
