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Jacobi Method; Simple system of equations

  1. Mar 16, 2008 #1
    I know this is simple, and I am missing something obvious. I'm suposed to use the "jacobi method"; and with each iteration it should be getting closer and closer to the solution (x=2 and y=1, which it is not). Could someone explain what I'm doing wrong, or how to start?
    [​IMG]
     
  2. jcsd
  3. Mar 17, 2008 #2
    If you do it using matrices, you'll get the coefficient matrix

    [tex]\displaystyle T=\begin{pmatrix} 0 & -\frac{1}{2}\\ 1 & 0 \end{pmatrix} [/tex]
    and
    [tex] c = \begin{pmatrix} 2.5\\-1\end{pmatrix}[/tex]

    Then you can evaluate each iteration via

    [tex] \displaystyle x_{k+1} = T x_k + c [/tex]

    where k+1 is your iteration number, and by looking at your work, you've chosen (0,0) to be your initial guess. I'm not too sure the numbers match up with what you've shown, but give it a try.
     
  4. Mar 17, 2008 #3
    Using a small program in MatLab, I found that in order to be accurate to within 2 decimal places, it requires about 19 iterations. 3 decimal places took 26 iterations, and 4 decimal places takes about 46. Needless to say, it doesn't converge very quickly.
     
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