## Definition of Interpolation

Given the set of tabular values (x0, y0), (x1, y1),…,(xn, yn) satisfying the relation y=f(x) where the explicit nature of f(x) is not known, it is required to find a simpler function say ?(x), such that f(x) and ?(x) agree at the set of tabulated points. Such a process is called as interpolation.

If we know ‘n’ values of a function, we can get a polynomial of degree (n-1) whose graph passes through the corresponding points. Such a polynomial is used to estimate the values of the function at the values of x.

We will study two different interpolation formula based on finite differences when the values of x are equally spaced. The first formula is:

Newton’s forward difference interpolation formula:

The formula is stated as:

Where ‘a+ph’ is the value for which the value of the function f(x) is to be estimated. Here ‘a’ is the initial value of x and ‘h’ is the interval of differencing.

## Question

The table gives the distance between nautical miles of the visible horizon for the given height in feet above the earth surface. Find the value of y when x= 218 feet.

## MATLAB Program for Newtons Forward Interpolation Formula

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