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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