# Thread: Thomas decomposition vs Cholesky decomposition

1. ## 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 ??

2. ## Re: Thomas decomposition vs Cholesky decomposition

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