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From: | Moritz Borgmann |
Subject: | Re: QR factorization |
Date: | Fri, 28 Mar 2008 21:04:48 +0100 |
Hi all. If you try the following with Octave 3.0.0+ octave:1> A=ones(3,4); octave:2> [Q,R]=qr(A); you get octave:3> Q Q = -0.57735 0.81650 0.00000 -0.57735 -0.40825 -0.70711 -0.57735 -0.40825 0.70711 With the other program, you get Q = -0.5774 -0.5774 -0.5774 -0.5774 0.7887 -0.2113 -0.5774 -0.2113 0.7887 and the same R. Both the factorizations satisfy Q*R=A and Q'*Q=eye(3) and both the programs claim to use the LAPACK routines DGEQRF and DORGQR. Where could be the difference?
look at the R matrix. Because A is rank-1, R has only one nonzero row (the first). Thus, the second and third columns of Q can be chosen arbitrarily as long as the columns of Q are orthonormal. There is simply no unique solution.
-M
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