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**Cubic Spline....what is the logic in constructing it?**

Hey guys,

I am not trying to directly code a cubic spline computation, but I am writing a sub routine in VBA that takes input data, and outputs it to a text file in Maple syntax.

Anywho, my cubic spline actually produces LINEAR splines!!! I can't figure out what is wrong with my logic?!

Here is my logic:

Suppose I have

**n**data points

Then I will have n-1 splines, defined for interval

**(x_i, x_(i+1))**where

*i = 1 to (n-1)*

I am modeling the spline according to the equation

**ax^3 + bx^2 + cx + d**,

and therefore IN TOTAL I will have

**4*(n-1)**different coefficients. The reasoning behind that is simple. The first spline has 4 coefficients, the second has 4, etc, and there are (n-1) splines in total.

I am also setting the first and second derivatives equal to zero (and hence equal to each other) at

**(x_i)**and

**(x_(i+1))**

So, here is what I am constraining each spline to:

**a(x_i)^3 + b(x_i)^2 + c(x_i) + d = y(x_i)**

**a(x_(i+1))^3 + b(x_(i+1))^2 + c(x_(i+1)) + d = y(x_(i+1))**

**3a(x_i)^2 + 2b(x_i) + c = 3a(x_(i+1))^2 + 2b(x_(i+1)) + c**

**6a(x_i) + 2b = 6a(x_(i+1)) + 2b**

So for example, suppose My points are: (-1,.5), (0,0) , (3,3)

I get the following function:

**S(x) = (-.5x, -1<x<0**

= ( x, 0<x<3

= ( x, 0<x<3

Where is my logic flawed? I would really appreciate any help.

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