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Thread: Thomas decomposition vs Cholesky decomposition

  1. #1
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    Thomas decomposition vs Cholesky decomposition

    x1 -x2 = 6
    3x1 +2x2 -2x3 = 2
    8x2 +3x3 = 6

    = $$\begin{bmatrix}
    1 & -1& 0 & |6 \\
    3 & 2 & -2 & |2 \\
    0 & 8 & 3 & |6
    \end {bmatrix} $$

    5x1 + 2x2 = 2
    2x1 + 5x2 + 2x3 = 2
    2x2 + 5x3 = 8

    = $$\begin{bmatrix}
    5 & 2& 0 & |2 \\
    2 & 5 & 2 & |2 \\
    0 & 2 & 5 & |8
    \end {bmatrix} $$

    I am given two sets of question ... In the first one , we can notice that the leading diagonal a11 , a22 and a33 are not the same , SO,
    I'm asked to solve it using Thomas method ,

    For the second one , We can notice that all the leading diagonal a11 , a22 and a33 are the same ,
    So , I 'm asked to solve it using Cholesky decomposition method ...

    For the second one , why must we use Cholesky method to solve ? In my book , it's not stated that
    for Cholesky method , all the leading diagonal must be the same ...

    I dont understand , can someone help to explain about it ? Why cant I solve the second question with Thomas method ??
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  2. #2
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    Re: Thomas decomposition vs Cholesky decomposition

    For the second matrix , can i use thomas method to solve it?
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