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# Approximation of Functions

DOI link for Approximation of Functions

Approximation of Functions book

# Approximation of Functions

DOI link for Approximation of Functions

Approximation of Functions book

## ABSTRACT

In this chapter, we are interested in approximation problems. For evaluating a function f(x) on a computer, in the context of space and time complexity, it is obviously better to have an analytic approximation to f(x) rather than to store a table and use interpolation because the computational overhead in function evaluation through interpolation techniques over stored tabular values is much higher in comparison to the use of efficient function approximations. Generally speaking, starting from a function f(x), we would like to find a different function ϕ(x) that belongs to a given class of functions and is close to f(x) in some sense. As far as the class of functions that ϕ(x) belongs to, we will typically assume that ϕ(x) is a polynomial of a given degree (though it can be a trigonometric function or any other function). It is desirable to use the lowest possible degree of polynomial that will give the desired accuracy in approximating f(x). A typical approximation problem will be therefore to find the closest polynomial of degree less than equal to f(x).