Re: Orthogonazlie with Method->"Householder"
- To: mathgroup at smc.vnet.net
- Subject: [mg97791] Re: Orthogonazlie with Method->"Householder"
- From: ADL <alberto.dilullo at tiscali.it>
- Date: Sun, 22 Mar 2009 05:44:58 -0500 (EST)
- References: <gpvh97$grj$1@smc.vnet.net>
Maris, I did the following computations also using the Rationalize version of your matrix: In[1]:= ClearAll[M, oM, MR, oMR]; In[2]:= M = {...}; (* deleted from the post *) In[3]:= MR = Rationalize[M, 10^(-16)]; oMR = Orthogonalize[MR]; In[5]:= methods = {"GramSchmidt", "ModifiedGramSchmidt", "Householder", "Reorthogonalization"}; In[6]:= (oM[#] = Orthogonalize[M, Method -> #]) & /@ methods; In[7]:= MatrixRank[oMR] Out[7]= 6 In[8]:= MatrixRank[oM[#]] & /@ methods Out[8]= {6,6,12,6} In[9]:= Chop@Max@Abs@(oM[#] - oMR) & /@ methods Out[9]= {0,0,1.23961912632296,0} In[10]:= $Version Out[10]= 7.0 for Microsoft Windows (32-bit) (February 18, 2009) >From this, I would say that the issue is not accuracy but the fact that "Householder" is not working properly. If it is a feature, it is a discount feature: you get 12 at the price of 6. What do you think about starting the famous "bugs and caveats" site with this post? ADL Maris Ozols ha scritto: > I have a large numeric matrix M (see below), whose rank is 6. Clearly, > the rank of Orthogonalize[M] must be the same (in particular, it > should not increase). However, if I execute the following code on my > matrix M: > > MatrixRank@M > MatrixRank@Orthogonalize[M] > MatrixRank@Orthogonalize[M,Method->"Householder"] > > I get 6, 6, and 12. So it appears to me that Householder's method has > doubled the rank of M. I am using Mathematica 7.0 in Linux. > > Is this a bug or a feature? > > ~Maris Ozols~
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