Discrete Approximation of Linear Functionals
Volume 2, Issue 2
Jack K. Cohen, Colorado School of Mines
David R. DeBaun, Unocal Corporation
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.