🚀 go-pugleaf

In article <17229@sophia.inria.fr> falzon@sophia.inria.fr writes:
>
> Does anybody have the general forms of eigenvalues and eigenvectors of an NxN
> pseudo-tridiagonal matrix of the form :
> 
> For example with N=4;
> 
>
>	[(1+1/a) -1/a       0         0 ]
>  A = 	[-1/a    (1+2/a)  -1/a        0 ]
>	[ 0       -1/a    (1+2/a)  -1/a ]
>	[ 0         0      -1/a  (1+1/a)] 
>
> Thanks in advance.
>
>
>      Fred.
>-----------------------------------------------------------------------------------------


Let me take this moment to recommend one of those old books lying
on the hard-to reach shelves of your library. 1966 "A collection of 
Matrices for Testing Computational Algorithms" by Robert T. Gregory and
David L. Karney by Wiley-Interscience. The book is dedicated to
A. S. Householder and it lives up to its title. 

I am certain (100%) that you will find the eigenvalues and eigenfunctions
to the matrix which is apparently from a second order central difference
finite difference discretization. It is a circulant matrix and have eigen
solutions which can be expressed in terms of bunch of cosines and sines. 
Contact me if you are still at loss. 

Ferhat 

-- 
Ferhat F. Hatay                        || Disclamer: |||||||||||||||||
Aerospace Engineering Sciences         || I speak for myself unless || 
University of Colorado, Boulder        || otherwise indicated.      ||
e-mail: hatay@spot.colorado.edu        |||||||||||||||||||||||||||||||