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Re: Orthogonazlie with Method->"Householder"

  • To: mathgroup at smc.vnet.net
  • Subject: [mg97781] Re: [mg97744] Orthogonazlie with Method->"Householder"
  • From: Maris Ozols <marozols at gmail.com>
  • Date: Sat, 21 Mar 2009 05:19:18 -0500 (EST)
  • References: <200903200740.CAA17270@smc.vnet.net> <49C40120.2020701@wolfram.com>

Sorry for sending such a large numeric matrix as plain text in my
e-mail. Singular values mentioned in both replies indicate that you
didn't succeed in recovering it correctly. So I sent my notebook in
attachment to Daniel Lichtblau and he confirmed the bad behavior of
Orthogonalize[M,Method->"Householder"] and filled a bug report.

Sorry for the confusion,

~Maris Ozols~

> 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

> [I recopy the matrix below, since my email reader showed something that was
> messed up a bit. --dl]
>
> In[2]:= InputForm[SingularValueList[mat]]
> Out[2]//InputForm=
> {7.053736007427739*^14, 44.4483160745624, 40.569302085579835,
> 25.471811796860234, 17.698020291765765}


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