From bug-octave-request at bevo dot che dot wisc dot edu Thu Jan 1 11:41:25 2004 Subject: Bad octave norms From: Vic Norton To: Date: Thu, 1 Jan 2004 04:24:55 -0600 The 1 and inf octave norms are not defined correctly for row vectors. The definitions should be norm(A, 1) = max(abs(A)) norm(A, inf) = sum(abs(A)) when rows(A) = 1. A reasonable matrix norm should satisfy norm(A * B) <= norm(A) * norm(B). The 1 and inf octave norms can violate this condition when A is a row vector. For example, set A = [1 0] and B = [1 1; 0 0]. Then 2 = norm(A * B, 1) > norm(A, 1) * norm(B, 1) = 1. Again, set A = [1 1] and B = [1 0; 1 0]. Then 2 = norm(A * B, inf) > norm(A, inf) * norm(B, inf) = 1. Regards, Vic ------------------------------------------------------------- Octave is freely available under the terms of the GNU GPL. Octave's home on the web: http://www.octave.org How to fund new projects: http://www.octave.org/funding.html Subscription information: http://www.octave.org/archive.html -------------------------------------------------------------