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Re: Orthogonazlie with Method->"Householder"

  • To: mathgroup at smc.vnet.net
  • Subject: [mg97788] Re: Orthogonazlie with Method->"Householder"
  • From: dh <dh at metrohm.com>
  • Date: Sat, 21 Mar 2009 05:20:36 -0500 (EST)
  • References: <gpvh97$grj$1@smc.vnet.net>


Hi Maris,

my giuess is that you run into numerical problems becaus of machine 

numbers. Consider the singular values of your matrix:

{1.75663*10^15, 2.21874*10^12,

  5.16322*10^10, 488354., 6518.66, 83.9465}

and you will see that 16 decimal digits may lead to problems.

If you calculate with exact numbers you will not have this problem.

But be aware, simply rationalizing your matrix introduces some error and 

can make linear depend vectors independent.

Daniel





Maris Ozols wrote:

> 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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