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MathGroup Archive 2004

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Re: finding eigenvalues

  • To: mathgroup at smc.vnet.net
  • Subject: [mg45487] Re: [mg45459] finding eigenvalues
  • From: "Sseziwa Mukasa,,(978) 536-2359" <mukasa at jeol.com>
  • Date: Sat, 10 Jan 2004 00:00:34 -0500 (EST)
  • References: <200401091020.FAA24586@smc.vnet.net>
  • Sender: owner-wri-mathgroup at wolfram.com

On Jan 9, 2004, at 5:20 AM, Jeremy Watts wrote:

> I have been wondering on whether there exist methods to find the 
> eigenvalues
> of a matrix other than solving the characteristic polynomial equation. 
>  Do
> there exist elementary row operation methods that will find the real
> eigenvalues of a matrix?
>
> I have been using a site that will find the eigenvalues of a matrix 
> and I'm
> wondering how it does it because I'm pretty sure its not doing it by 
> solving
> the characteristic equation.

Traditionally, eigenvalues are found by reducing a matrix to triangular 
form rather than solving the characteristic equation.  For information 
on some numerical methods for finding eigenvalues you can read 
Numerical Recipes chapter 11 which can be found at www.nr.com, or for a 
more detailed explanation see Golub and Van Loan's Matrix Computations. 
  Finding the eigenvalues is computationally intensive and even more 
difficult if eigenvectors are desired, there are a simplifications 
possible in the case of symmetric or Hermitian matrices.

Regards,

Ssezi


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