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Math Help - Cubic Hermite interpolation given some data

  1. #1
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    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

    The last divided difference is \frac{-0.095 - (-0.0075)}{13-0} = -0.00673


    Now, I wrote the polynomial as 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...



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  2. #2
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    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?
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  3. #3
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    Re: Cubic Hermite interpolation given some data

    Quote Originally Posted by chiro View Post
    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!
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  4. #4
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    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?
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