Mth Order Piecewise Spline Interpolation

GSP is a graphical user interface which takes x and y points as inputs, along with the order m, then outputs mth order splines between each of the x points. In most cases additional constraints are to be entered as well.

Example:

Input:

x points : [1 2 3 4]
y points : [2 7 -1 5]
Order : 2
*One Additional Constraint is Required*
f '' (1) = 0

Output:

Polynomials:
0 5 -3
-13 57 -55
27 -183 305

In the Range:
1 2
2 3
3 4

This means the following:

for 1 < x < 2 y = 0*x^2 + 5*x - 3
for 2 < x < 3 y = -13*x^2 + 57*x - 55
for 3 < x < 4 y = 27*x^2 - 183*x + 305