Question 1046540
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For some useful info related to this subject see this Wikipedia article


<A HREF=https://en.wikipedia.org/wiki/Cholesky_decomposition>https://en.wikipedia.org/wiki/Cholesky_decomposition</A>


https://en.wikipedia.org/wiki/Cholesky_decomposition



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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.  
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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

   &nbsp;&nbsp;&nbsp;&nbsp;- "Numerical recipies, vol. I"   &nbsp;&nbsp;&nbsp;&nbsp;(classic)
   &nbsp;&nbsp;&nbsp;&nbsp;- "LINPACK user's guide" (1979) by Dongarra and others . . . &nbsp;&nbsp;&nbsp;&nbsp;(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 

<A HREF=http://comnuan.com/cmnn0100d/>http://comnuan.com/cmnn0100d/</A>


http://comnuan.com/cmnn0100d/