Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Calculate quintic spline with Gauss Seibel

  1. Sep 29, 2010 #1
    In java, I am trying to implement algorithm found here:
    http://books.google.com/books?id=kY...9_EIHAvEi9bLZ6lC7s1mdtg3I#v=onepage&q&f=false

    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
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook

Can you offer guidance or do you also need help?
Draft saved Draft deleted