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Re: LUDecomposition output?

• Subject: [mg2623] Re: LUDecomposition output?
• From: danl (Daniel Lichtblau)
• Date: Thu, 30 Nov 1995 20:59:20 -0500
• Approved: usenet@wri.com
• Distribution: local
• Newsgroups: wri.mathgroup
• Organization: Wolfram Research, Inc.

In article <49dojj$8a6 at dragonfly.wri.com> buchan at metronet.com (John S.  
Buchan) writes:
> Can someone tell me how, exactly, is the LUDecomposition output  
formatted?
> I have a symmetric matrix which I need to decompose into a lower and an  
upper
> diagonal matrix, but I cannot find any reference to the command itself.  
> Executing LUDecomposition[ ] gives me a single table, but I do not know  
which 
> coefficents belong to which matrix.  Any help will be appreciated.
> 

  The first element returned is a matrix containing the factorization  
itself, and the second element is the list of permutations, that is, row  
exchanges, used during the Gaussian elimination process. They are  
relative, not absolute. Specifically, the value k in the jth entry means  
that what was row k at the time row j was processed (not necessarily  
initially) became row j.
  For the factorization, we record the upper triangular matrix as the  
diagonal-and-above part. Below the diagonal we store the multipliers  
comprising the lower diagonal matrix less its main diagonal, which  
consists of ones.
  This is spelled out in some detail in the LINPACK User's Guide by  
Dongarra et al, in the first chapter, around p. 1.10. Our code uses the  
LINPACK technology. With a bit of patience you can work out the conversion  
details involving the explicit construction of the permuted lower  
triangular matrix.

  Daniel Lichtblau
  Wolfram Research, Inc.