Engineering Mathematics, Volume 2

4

Interpolation

4.1 Introduction

Let the values of a function y = f(x) be given at different x values; thus,

 

 

Then interpolation means to find an approximate value of f(x) for an x between two x-values in (x₀, x_n). This is done by finding a polynomial called an interpolating polynomial which agrees with the function at the nodal points x_i (i = 0, 1, 2, …, n). In finding a suitable interpolating polynomial we need to have a formula for errors in polynomial approximation.

4.1.1 Formula for Errors in Polynomial Interpolation

Let y = f(x) be a function defined at the (n + 1) points

 

(x_i, y_i) (i = 0, 1, 2, …, n)     (4.1)

 

 

 

Suppose f(x) is ...