Discrete Approximation of Linear Functionals

Volume 2, Issue 2
1992

Obtaining finite difference approximations using function values at equally spaced sample points is an important problem in numerical analysis. A familiar example is Simpson's Rule for numerical integration. Finite difference approximations for operators such as definite integration, interpolation, and differentiation are all special cases of linear functionals. The algorithm presented here solves the approximation problem for an arbitrary linear functional. We give a simple Mathematica implementation for dimensions one, two, and three.