Numerical Methods and Optimization

Chapter 5

Polynomial Interpolation

Many problems arising in engineering require evaluation of real-valued func-

tions. Evaluation of some of the commonly used functions, such as cos(x), on

a computer usually utilizes the so-called lookup tables, which store a finite

set of numbers describing the function of interest in a way that allows one to

approximate the value of f(x) for any given x with a high level of accuracy.

For example, a finite set of coefficients in the power series decomposition of

f(x) could be used for this purpose.

Example 5.1 Consider f(x) = cos(x),x ∈ [−1, 1]. The Taylor series approx-

imation of this function about the origin is

cos(