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Re: slow eigenvectors and eigenvalues

• To: mathgroup at smc.vnet.net
• Subject: [mg52974] Re: slow eigenvectors and eigenvalues
• From: "Steve Luttrell" <steve_usenet at _removemefirst_luttrell.org.uk>
• Date: Sat, 18 Dec 2004 03:59:57 -0500 (EST)
• References: <cpueev$gc5$1@smc.vnet.net>
• Sender: owner-wri-mathgroup at wolfram.com

The eigenvectors of a Toeplitz matrix (a very large one, so that the edge 
effects can be ignored) is made up of sine waves. This is because the left 
hand side of the eigenequation T.x=a x is a convolution, so if you transform 
to Fourier space it is a multiplication (i.e. the convolution theorem), 
which is a diagonal operation whose eigenvectors are the individual Fourier 
components.

Steve Luttrell

"Janusz" <janus at sci.pam.szczecin.pl> wrote in message 
news:cpueev$gc5$1 at smc.vnet.net...
> Hello!
>
> I need eigenvectors and eigenvalues of Toeplitz matrix 1000 by 1000 or
> greater. These are values of autocorrelation of processed signal. My
> Version 5. does it for a long time. After a few hours I aborted
> calculations. What should I do to make it faster?
>
> Thanks in Advance
> Regards
>
> Janusz Kowalski
> Szczecin, Poland
>