Polynomial Curve Fitting

Suppose a collection of data is represented by n points in the xy-plane,

          ( x1 , y1 ),   ( x2 , y2 ) ,..., ( x n , yn )

and you are asked to find a polynomial function of degree n-1

          p(x) = a0 + a1x + a2x2 + ... + an-1xn-1

whose graph passes through the specified points. This procedure is polynomial curve fitting. If all x-coordinates of the points are distinct, then there is precisely one polynomial function of degree n-1 that fits the n points.

     To solve for the n coefficients of p(x), substitute each of the n points into the polynomial function and obtain n linear equations in n variables.

EXAMPLE: