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Cholesky method

  1. Mar 1, 2017 #1
    1. The problem statement, all variables and given/known data
    For the choelsky method , i was told by my lecturer that all the leading diagonal a11 , a22 and a33 must be the same... But , when I tried to find online resources , I found that that it's not stated in the rule that the leading diagonal a11 , a22 and a33 must be the same ...
    5x1 + 2x2 = 2
    2x1 + 5x2 + 2x3 = 2
    2x2 + 5x3 = 8
    In this example , I was told that it cant be solved by Thomas method ( can only be solved by Cholesky method) although the a13 and a31 = 0 ... ( According to Thomas method , the matrix a13 and a31 must be 0 )
    $$\begin{bmatrix}
    5 & 2& 0 & 2 \\
    2 & 2 & 2 & 2 \\
    0 & 2 & 5 & 8
    \end {bmatrix} $$

    https://en.wikipedia.org/wiki/Cholesky_decomposition

    https://en.wikipedia.org/wiki/Tridiagonal_matrix_algorithm
    2. Relevant equations


    3. The attempt at a solution


    So , I think that my lecture's is wrong . I think for Cholesky method that the a11 , a22 and a33 can or cannot be the same ..

    I think the above equation can also be solved by Thomas method
     
    Last edited: Mar 1, 2017
  2. jcsd
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