1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

I don't fully understand this question about cubic spline interpolation

  1. Oct 23, 2011 #1
    8wck6e.png

    If each spline is given in the form of

    gi(x) = ai(x-xi)3 + bi(x-xi)2 + ci(x-xi) + di

    where i = 1 to N for N+1 data points.

    Then given that b1 and bN+1 are zero (because the second derivatives are zero at the endpoints, due to this being a natural cubic spline), then there are N-1 equations for b2....bN.

    Since we then use the value of bi to work out the unknowns ai, ci and di then there are four equations per i. Then since bi and bN+1 are zero, we can work out ai, ci and di on the last splines (3 each).

    So is the answer 4(N-1) +6?

    I don't understand what it means by 'Show there are enough equations..', any ideas?

    Thanks
     
  2. jcsd
  3. Oct 23, 2011 #2

    I like Serena

    User Avatar
    Homework Helper

    Hi Firepanda! :smile:

    If you have N+1 datapoints, that means you have N cubic splines.
    Each spline has 4 unknown parameters for a total of 4N parameters.
    To solve all parameters you need as many equations as parameters.

    So you need exactly 4N equations...
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: I don't fully understand this question about cubic spline interpolation
  1. Cubic spline question (Replies: 8)

Loading...