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For some useful info related to this subject see this Wikipedia article
https://en.wikipedia.org/wiki/Cholesky_decomposition
https://en.wikipedia.org/wiki/Cholesky_decomposition
Somewhere in the beginning of 80-ies I was in need to have my own computer program (subroutine) based on this algorithm
(Cholesky LU-decomposition) to use it in the more wide finite element code for solving systems of linear equations.
I was lucky: I found very good description of the algorithm in the book by Wilkinson and Reinsch "Handbook for Automatic Computations".
I learned this algorithm, wrote the subroutine, wrote the entire finite-element code and used it during some years,
making my research computer simulations.
It worked successfully in solving matrix equations of the size 1000 - 3000 - 5000 in one (in each of the two) matrix dimensions.
For more grandiose matrices the algorithm lost its effectiveness, and other methods were required.
Some reminiscences . . .
Surely, I know the algorithm, but its presentation requires a lot of writing.
This is why I refer you to that article.
See also in the Internet with keywords "Cholesky decomposition", "LU-decomposition" . . .
Also, good sources of information are the books
- "Numerical recipies, vol. I" (classic)
- "LINPACK user's guide" (1979) by Dongarra and others . . . (classic too)
As well as any authoritative contemporary guide/textbook on Matrix Computations.
In nowadays, you can even find an online matrix calculator in the Internet making LU-decomposition for free ! ! !
I just found one such a calculator for you under the link
http://comnuan.com/cmnn0100d/
http://comnuan.com/cmnn0100d/