From mboxrd@z Thu Jan 1 00:00:00 1970 Return-Path: Received: (qmail 23230 invoked by alias); 22 Oct 2002 10:02:14 -0000 Mailing-List: contact gsl-discuss-help@sources.redhat.com; run by ezmlm Precedence: bulk List-Subscribe: List-Archive: List-Post: List-Help: , Sender: gsl-discuss-owner@sources.redhat.com Received: (qmail 23215 invoked from network); 22 Oct 2002 10:02:12 -0000 Received: from unknown (HELO viadrina.euv-frankfurt-o.de) (193.174.120.1) by sources.redhat.com with SMTP; 22 Oct 2002 10:02:12 -0000 Received: from euv-frankfurt-o.de (ab-42125.euv-frankfurt-o.de [10.173.42.125]) by viadrina.euv-frankfurt-o.de (8.12.1/8.12.1) with ESMTP id g9MA2AJh020006 for ; Tue, 22 Oct 2002 12:02:10 +0200 (MET DST) Message-ID: <3DB521DE.2020006@euv-frankfurt-o.de> Date: Tue, 22 Oct 2002 03:12:00 -0000 From: Przemyslaw Sliwa User-Agent: Mozilla/5.0 (X11; U; Linux i686; en-US; rv:1.0.1) Gecko/20020826 X-Accept-Language: en-us, en MIME-Version: 1.0 To: gsl-discuss@sources.redhat.com Subject: Determinant of a matrix Content-Type: text/plain; charset=us-ascii; format=flowed Content-Transfer-Encoding: 7bit X-SW-Source: 2002-q4/txt/msg00065.txt.bz2 Hello, The determinant of a symmetric positive definite matrix is just the product of the squares of the diagonal elements form the cholesky decomposition (NAG documentation). So why I'm getting different results form gsl_LU decomposition and the cholesky decomposition of a 10*10 Hilbert matrix (elemenst i,j given by 1/(i+j-1)). The results are not very big, but still they exist (determinant about 0.5E+13 and the difference 6.0E+1). Is it a bug, or the LU decomposition is unstable. What should be suggested: determinant of a covariance matrix: its Cholesky form or computation from LU decomposition. Thanks for help Przem