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

  1. Oct 23, 2011 #1

    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?

  2. jcsd
  3. Oct 23, 2011 #2

    I like Serena

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    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...
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