Advanced Mathematics For Engineering and Science
As the product of a close collaboration between two mathematicians and an engineer, this pragmatic text provides the know-how and know-why to understanding mathematics and its many applications.
TABLE OF CONTENTS Advanced Mathematics For Engineering and Science
7.6: INTERPOLATION
7.6 INTERPOLATION
In this section, we address the following problem. We wish to estimate the value of f(x) for some x in the interval (x 0, x n), given a collection of experimental data points [x k, f(x k)], k=0, 1, , n. This problem has been studied by well known mathematicians such as Gauss, Lagrange, and Newton. The earliest method requires one to fit a polynomial (an interpolation function) that approximates the function f over (x 0, x n) or a curve that passes through the data points. The points x k are sometimes called the nodes.
Lagrange Interpolation
This method is based on choosing a polynomial p n(x) of degree n for which
| (7.6 1) |  |
An existence theorem for polynomial interpolation states that given (n+1) points {x 0, x 1, , x n} in the domain of a function f with n ?1 and x 0
A polynomial of degree one (linear polynomial) has the form
| (7.6 2) |  |
This equation has two coefficients and, therefore, two points (x 0, f 0) and (x 1,...
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