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[Octave-bug-tracker] [bug #41116] Incorrect result for sparse LU factori

From: Michael C. Grant
Subject: [Octave-bug-tracker] [bug #41116] Incorrect result for sparse LU factorization
Date: Tue, 14 Jan 2014 14:03:55 +0000
User-agent: Mozilla/5.0 (Macintosh; Intel Mac OS X 10_9_1) AppleWebKit/537.73.11 (KHTML, like Gecko) Version/7.0.1 Safari/537.73.11

Follow-up Comment #12, bug #41116 (project octave):

Hmm, you might be right. Here's the documentation: " [L,U,P] = lu(A) returns
unit lower triangular matrix L, upper triangular matrix U, and permutation
matrix P so that P*A = L*U."

For this particular value of x, you're right, even with the column
permutations, the upper triangular property is preserved. My concern was that
there might be scenarios where the column permutations would destroy the upper
triangular property of the matrix.

Certainly, it is possible for an *arbitrary* upper triangular matrix U2 and an
*arbitrary* column permutation Q2 that the matrix U=U2*Q2' would fail to be
upper triangular. But perhaps the way UMFPACK chooses its numerical swaps,
this would not happen.


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