3.2.1 Global polynomial
In this method a smooth surface is fitted using a polynomial function on
the basis of input points. There is a gradual change in the surface.
This method can be assumed as fitting a piece of paper between the
plotted points; these points are elevated points, elevation being equal
to their respective values. It’s obvious that the paper will not pass
through all the points. There will be a few sets of points which shall
not lie on the paper. There are some points which are above and some
which are below the paper. However, when we measure the height by which
the points are raised above the paper and take the summation of all such
points, it is found that this summation is equal to the summation of
height of all points falling below the surface of the paper.
The interpolating polynomial is as follows:
\(P\left(x_{k}\right)=\sum_{i=0}^{n-1}{a_{i}x_{k}^{i}}\) (1) 1
Where \(P\left(x_{k}\right)\) is the interpolating polynomial for n
distinct points
(x k, f k)