# Cholesky method

1. Mar 1, 2017

### fonseh

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