Remainders in Interpolation and Quadrature Formulae

Abstract

The determination of the errors involved in interpolation or quadrature formulae often involves complicated reasoning. There are many cases, however, where the remainder can be obtained very easily. These cases belong to the class which we call simplex.In general a formula will be expressible in the formL(f) =∑rArf(xr) + ∑sBsf'(xs)+ ∑tCtf''(xt) +… ......(1)to a finite number of terms and it is assumed throughout that f(x) possesses derivatives as far as the remainder may require.