# Cubic Hermite interpolation given some data

• Oct 27th 2012, 02:14 PM
jwxie
Cubic Hermite interpolation given some data
 Time Distance Speed 0 0 75 3 225 77 5 383 80 8 623 74 13 993 72

Question: Use cubic Hermite interpolation to predict the position of the car and its speed when t = 10s.

My work
http://i.imgur.com/WQWW6.png
The last divided difference is $\displaystyle \frac{-0.095 - (-0.0075)}{13-0} = -0.00673$

Now, I wrote the polynomial as $\displaystyle 75 + 0.8x - 0.0075x(x-3) - 0.00673x(x-3)(x-5)$

I evaluated this at t=10s but it came out to be around 77. If we plugged it into the previous polynomial, 77 would be too small.... even if it was speed, it looked wrong to me because the speed at t=10s is decreasing...

• Oct 27th 2012, 06:23 PM
chiro
Re: Cubic Hermite interpolation given some data
Hey jwxie.

You are mentioning two polynomials in your question but I can only see one which your Hermite approximation for the first three data points. Is there another polynomial you are comparing this Hermite one with?
• Oct 27th 2012, 07:08 PM
jwxie
Re: Cubic Hermite interpolation given some data
Quote:

Originally Posted by chiro
Hey jwxie.

You are mentioning two polynomials in your question but I can only see one which your Hermite approximation for the first three data points. Is there another polynomial you are comparing this Hermite one with?

I think the polynomial I wrote at the end was for the position. The f prime of that would be the speed...

but then again, if i plugged in 10 as x into the polynomial, the answer came out to be 77. If that was distance, it wouldn't make sense.... thanks!
• Oct 27th 2012, 09:00 PM
chiro
Re: Cubic Hermite interpolation given some data
Just out of curiosity, can you plot the polynomial and the data points belonging to your original sample?