In this paper we investigate the L^2 piecewise polynomial approximation problem. L^2 bounds for the derivatives of the error in approximating sufficiently smooth functions by polynomial splines follow immediately from the analogous results for polynomial spline interpolation. We derive L^2 bounds for the errors introduced by the use of two types of quadrature rules for the numerical computation of L^2 piecewise polynomial approximations. These bounds enable us to present some asymptotic results and to examine the consistent convergence of appropriately chosen sequences of such approximations. Some numerical results are also included.ududud
展开▼
机译：在本文中，我们研究了L ^ 2分段多项式逼近问题。从多项式样条插值的相似结果中可以立即得出误差的导数的L ^ 2边界，该近似值由多项式样条近似。我们通过使用两种正交规则对L ^ 2分段多项式逼近进行数值计算而引入的误差得出L ^ 2界。这些界限使我们能够呈现一些渐近结果，并检查适当选择的此类近似序列的一致收敛性。也包括一些数值结果。 ud ud ud
展开▼
