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Calculate quintic spline with Gauss Seibel

  1. Sep 29, 2010 #1
    In java, I am trying to implement algorithm found here:

    The goal is to take a list of points and generate the quintic spline, then be able to get a point at any time within the dataset.

    From what I can tell, given:
    Xi(T) = Ai(T-Ti)^5 + Bi(T-Ti)^4 + Ci(T-Ti)^3 + Di(T-Ti)^2 + Ei(T-Ti) + Fi

    The formula of A,B,C,D,E, and F become:

    Ai = 1/120(T(i+1) – Ti) * (X’’’’i * T(i+1))
    Bi = 1/24X’’’’i
    Ci = 1/6(T(i+1) – Ti) * (X’’(i+1) – X’’i) - (T(i+1) – Ti)/36 * (X’’’’(i+1) – 2X’’’’i)
    Di = 1/2P’’i
    Ei = 1 / (T(i+1) – Ti) * (X(i+1) – Xi) – 1/6 * (T(i+1) – Ti) * (X’’(i+1) – 2X’’i)
    + 1/360 * (T(i+1) – Ti)^3 * (7P’’’’(i+1) + 8 X’’’’i)
    Fi = Xi

    From here, the author seems to do a lot of simplification, then ends up at the matrices:

    [ A -B ] [ X’’ ] = [ d ]
    [ C A ] [ X’’’’ ] [ 0 ]

    The matrices are then supposed to be solved using the Gauss-Seibel method.

    I have the following questions:
    1. I think I understand Gauss-Seibel, but I don’t see how it applies to a tridiagonal array. Aren’t I only supposed to calculate pieces of the array? Then again, perhaps I don’t understand the Gauss-Seibel method.
    2. The formulae entered into the matrices seem to change with the index. I don’t understand this. Can someone explain.
    3. I really don’t know where to go from here in terms of a method of calculating the spline and getting a value.

    If anyone can point me in the right direction in terms of a method of solving the equation/calculating the spline, it would be much appreciated.

    Thank you in advance!
  2. jcsd
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