Path: news.mathworks.com!not-for-mail From: "Bruno Luong" <b.luong@fogale.findmycountry> Newsgroups: comp.soft-sys.matlab Subject: Re: Finding the nearest matrix with real eigenvalues Date: Fri, 3 Sep 2010 11:12:07 +0000 (UTC) Organization: FOGALE nanotech Lines: 17 Message-ID: <i5ql67$sp0$1@fred.mathworks.com> References: <i5j67v$4s4$1@fred.mathworks.com> <i5jicf$29u$1@fred.mathworks.com> <i5jn7k$pdd$1@fred.mathworks.com> <i5jvad$c2b$1@fred.mathworks.com> <i5p6tb$f0b$1@fred.mathworks.com> <i5p8sn$mid$1@fred.mathworks.com> <i5qi10$6oo$1@fred.mathworks.com> Reply-To: "Bruno Luong" <b.luong@fogale.findmycountry> NNTP-Posting-Host: webapp-02-blr.mathworks.com Content-Type: text/plain; charset=UTF-8; format=flowed Content-Transfer-Encoding: 8bit X-Trace: fred.mathworks.com 1283512327 29472 172.30.248.37 (3 Sep 2010 11:12:07 GMT) X-Complaints-To: news@mathworks.com NNTP-Posting-Date: Fri, 3 Sep 2010 11:12:07 +0000 (UTC) X-Newsreader: MATLAB Central Newsreader 390839 Xref: news.mathworks.com comp.soft-sys.matlab:667402 "Matt J " <mattjacREMOVE@THISieee.spam> wrote in message <i5qi10$6oo$1@fred.mathworks.com>... > "Bruno Luong" <b.luong@fogale.findmycountry> wrote in message <i5p8sn$mid$1@fred.mathworks.com>... > > Bruno, although there are "floating" things in this norm, i.e., the scaling of the eigenvalues, the solution is invariant to them. But that's even more disturbing. There is a family of "norms" that depends on scaling and the input, whereas the solution does not depend on the scaling. This solution cannot be *characterized* as the minimum of a "clean" cost function. The minimum of the norm is a property. I'll caricature here, but I could also tell: B = V'*real(D)*V, solution proposed by Roger, minimizes the cost function norm(Ap-B, 'fro') where Ap:=V'*real(D)*V, and [V D]=eig(A). That claims of course does not have any intrinsic value and it's certainly true. In a way you are doing more or less like this, you define a norm that is floating. Bruno