Theoretical Numerical Analysis pp 92-130 | Cite as

# Approximation Theory

Chapter

## Abstract

In this chapter, we deal with the problem of approximation of functions. A prototype problem can be described as follows: For some function The approximating functions need to be of simple form so that it is easy to make calculations with them. The most commonly used classes of approximating functions are the polynomials, piecewise polynomial functions, and trigonometric polynomials.

*f*, known exactly or approximately, find an approximation that has a more simply computable form, with the error of the approximation within a given error tolerance. Often the function*f*is not known exactly. For example, if the function comes from a physical experiment, we usually have a table of function values only. Even when a closed-form expression is available, it may happen that the expression is not easily computable, for example,$$ f(x) = \int_0^x {{e^{ - {t^2}}}} dt $$

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## Copyright information

© Springer-Verlag New York, Inc. 2001