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MathGroup Archive 2007

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Re: Eigensystem

  • To: mathgroup at smc.vnet.net
  • Subject: [mg73325] Re: [mg73309] Eigensystem
  • From: Bob Hanlon <hanlonr at cox.net>
  • Date: Mon, 12 Feb 2007 05:04:14 -0500 (EST)
  • Reply-to: hanlonr at cox.net

Eigensystem will maintain the precision of the least precise input. If you want high precision give it high precision inputs.

m={{1,2},{3,4}};

es=Eigensystem[m];

t=Transpose[es[[2]]];

Simplify[m.t-t.DiagonalMatrix[es[[1]]]]

{{0, 0}, {0, 0}}

m={{Random[Real,{0,1},50],
        Random[Real,{0,1},50]},
      {Random[Real,{0,1},50],
        Random[Real,{0,1},50]}};

es=Eigensystem[m];

t=Transpose[es[[2]]];

Simplify[m.t-t.DiagonalMatrix[es[[1]]]]

{{0``49.59034527615688, 0``49.83942922976429}, {0``49.58735034913213, 0``50.05028140987655}}

m={{Random[Real,{0,1},50],
        Random[Real,{0,1},35]},
      {Random[Real,{0,1},50],
        Random[Real,{0,1},50]}};

es=Eigensystem[m];

t=Transpose[es[[2]]];

Simplify[m.t-t.DiagonalMatrix[es[[1]]]]

{{0``34.91939782420133, 0``35.16524293662837}, {0``34.59030012679873, 0``34.92880488167243}}


Bob Hanlon

---- "Vadim N. Smelyanskiy" <vadim at email.arc.nasa.gov> wrote: 
> Dear Sir/Madam:
> 
>  
> 
> I am a user of Mathematica 5.2 for Windows.
> 
> Please can you advice me how to run Eigensystem function so that its result
> has precision (say 50)
> 
> that is much higher then the Machine Precision. 
> 
>  
> 
> Thank you
> 
> Vadim
> 
>  
> 
> Vadim N. Smelyanskiy, PhD
> 
> NASA Ames Research Center
> 
> Discovery and System Health Area
> 
> Intelligent Systems Division
> 
> Mail Stop 269-3
> 
> Moffett Field, CA 94035-1000
> 
> Tel.: 650-604-2261
> 
> Fax: 650-604-4036



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