Approximation and Interpolation

Walter Gautschi ()
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Walter Gautschi: Purdue University, Department of Computer Sciences

Chapter Chapter 2 in Numerical Analysis, 2012, pp 55-158 from Springer

Abstract: Abstract 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.

Keywords: Orthogonal Polynomial; Chebyshev Polynomial; Lagrange Interpolation; Divided Difference; Hermite Interpolation (search for similar items in EconPapers)
Date: 2012
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DOI: 10.1007/978-0-8176-8259-0_2

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