Methods of approximation theory

Ian Jacques and Colin Judd
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Ian Jacques: Coventry Lanchester Polytechnic, Department of Mathematics
Colin Judd: Coventry Lanchester Polytechnic, Department of Mathematics

Chapter 5 in Numerical Analysis, 1987, pp 129-189 from Springer

Abstract: Abstract In this chapter we describe some of the numerical methods that are used in approximation theory. The main purpose of these techniques is to replace a complicated function by one which is simpler and more manageable. The classes of approximating functions that are employed include polynomials, trigonometric functions and rational functions. However, we shall restrict our attention to polynomials. These are widely used in practice, since they are easy to evaluate, differentiate and integrate, and they are well behaved-all derivatives exist and are continuous. Whilst most of the techniques described in this chapter are of considerable practical value, some are also studied for their theoretical importance. In particular, the material on polynomial interpolation will be used in subsequent chapters to derive numerical methods for differentiation, integration and the solution of ordinary differential equations.

Date: 1987
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DOI: 10.1007/978-94-009-3157-2_5

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