Solving a Tridiagonal Matrix Using Cholesky and Thomas Methods

[fonseh]

Homework Statement

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 can't 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

Homework Equations

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 [/B]

 

[lippyka]

since it is a tridiagonal matrix and a13 and a31 = 0 . The Thomas method is an algorithm for solving tridiagonal systems of equations. A tridiagonal matrix is a matrix that has nonzero entries only on the main diagonal, the first diagonal below this, and the first diagonal above the main diagonal. So, a tridiagonal matrix must have a13 and a31 equal to 0.