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Discrete Approximation of Linear Functions

Jack K. Cohen
Organization: Center for Wave Phenomena, Colorado School of Mines
David DeBaun
Journal / Anthology

The Mathematica Journal
Year: 1992
Volume: 2
Issue: 2
Page range: 62-65

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 solved the approximation problem for an arbitrary linear functional. We give a simple Mathematica implementation for dimensions one, two, and three.

*Applied Mathematics > Numerical Methods
*Applied Mathematics > Numerical Methods > Approximation Theory