Approximation and Interpolation
The present chapter is basically concerned with the approximation of functions. The functions in question may be functions defined on a continuum – typically a finite interval –or functions defined only on a finite set of points. The first instance arises, for example, in the context of special functions (elementary or transcendental) that one wishes to evaluate as a part of a subroutine. Since any such evaluation must be reduced to a finite number of arithmetic operations, we must ultimately approximate the function by means of a polynomial or a rational function. The second instance is frequently encountered in the physical sciences when measurements are taken of a certain physical quantity as a function of some other physical quantity (such as time). In either case one wants to approximate the given function “as well as possible” in terms of other simpler functions.
KeywordsOrthogonal Polynomial Chebyshev Polynomial Lagrange Interpolation Divided Difference Hermite Interpolation
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