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## 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, xn). This is done by finding a polynomial called an interpolating polynomial which agrees with the function at the nodal points xi (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

(xi, yi) (i = 0, 1, 2, …, n)     (4.1)

Suppose f(x) is ...

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