Re: LUDecomposition output?

*To*: mathgroup at smc.vnet.net*Subject*: [mg2623] Re: LUDecomposition output?*From*: danl (Daniel Lichtblau)*Date*: Thu, 30 Nov 1995 20:59:20 -0500

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.