Construct a free cubic spline

1. Dec 12, 2005

stunner5000pt

Construct a free cubic spline to approximate f(x) = e^ -x , by using values for x = 0 , 0.25, 0.75, 1
now i know i have to contstruct something like this
$$ss_{j} = a_{j} + b_{j} (x - x_{j}) + c_{j} (x-x_{j})^2 + d_{j} (x- x_{j})^3$$
also we know from the initial conditions that a0 = f(0), but im not sure what to do after this...

I have to do this for each interval and in all there will be three splines (cubic polynomials) But i cannot find any of the a,b,c, or d s. My textbook doesnt help either... i wouldnt be asking this if it gave a good xample showing how it got the answer rather than show me a code for maple to find this! Perhaps you could direct me to a website that ilustrates how to a1,b1,c1, and so on ...
YOur hlep would be greatlly apprcietaetd since my exam is in about 5 hours... I

And yes i know this is last minute but i have consulted numerous books and all of that searhin ahs yielded nothing or use.

2. Dec 12, 2005

Staff: Mentor

I am sure this is too late to help you out, but my favorite two online resources are Wikipedia (http://en.wikipedia.org/wiki/Spline_interpolation[/url]) in general and MathWorld ([url]http://mathworld.wolfram.com/CubicSpline.html [Broken]) specifically for math questions.

-Good luck
Dale

Last edited by a moderator: Apr 21, 2017 at 10:24 PM