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MathGroup Archive 1996

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Re: Question

  • Subject: [mg2911] Re: Question
  • From: danl (Daniel Lichtblau)
  • Date: 9 Jan 1996 04:31:49 -0600
  • Approved: usenet@wri.com
  • Distribution: local
  • Newsgroups: wri.mathgroup
  • Organization: Wolfram Research, Inc.
  • Sender: mj at wri.com

In article <4cgrt5$im4 at dragonfly.wri.com> coppelli at sun3.dsea.unipi.it  
(Alessandro Coppelli) writes:
> 
> Hi to all.
> 
> 
>    Question for guru in mathematica:
> 
> 
>   1) If I have the problem  ..A x = lamba B x ..  with B singular which 
>      program I must be used for to find lamba
>  

  We do not have a built-in generalized eigenvalues routine. Here is a  
routine that will do the job, although the numeric stability might be  
questionable. 

genEigval[A_, B_, lam_] := Module[{n=Length[A], vals, gendet, rank},
    rank = Length[SingularValues[B][[2]]];
    vals = Map[Det[A-#*B]&, Table[j, {j, 1, rank+1}]];
    gendet = InterpolatingPolynomial[vals, lam];
    lam /. Solve[gendet==0, lam]
    ]


>   2) If I have the lamba matrix (  A(lamba) ) which program I must be  
used
>      for factoring A in  A(lamba)=H(lamba) *  
diag(P1(lamba).....Pn(lamba)) * K(lamba)
>      with H and K not singular matrix and Real

  I may not understand your question. Taking a guess, I'd say you probably  
want SingularValues[...].


>   3) If I have the lamba matrix which program I must be used for applied  
the 
>      method Gauss/Jordan on A(lamba)

  Again, I'm guessing. You perhaps want to use RowReduce[...].


  Daniel Lichtblau
  WRI


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