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Good eigenvalue/eigenvector test problems for eigs?

From: David Bateman
Subject: Good eigenvalue/eigenvector test problems for eigs?
Date: Fri, 22 Sep 2006 13:46:18 +0200
User-agent: Thunderbird (X11/20060817)

Does any one have a simple to create set of matrices of variable order
for symmetric, non-symmetric and complex problems for me to test my eigs
code against. Basically, it seems that the easy to create sparse
matrices that I can think of are all ill-conditioned and result in
incorrect results in many case. What I currently have is

## Symmetric real PD
 A = spdiags([ones(n,1),4*ones(n,1),ones(n,1)],[-2,0,2],n,n);
## Non-symmetric
A = spdiags([ones(n,1),4*ones(n,1),-ones(n,1)],[-2,0,2],n,n);
## Complex
A = spdiags([ones(n,1),4*ones(n,1),1i*ones(n,1)],[-2,0,2],n,n);

which as I say are ill-conditioned. So I'm looking for something as easy
to express as the above.. Apart from this issue, I appear to have a
relative complete eigs function now working (more info later)...


David Bateman                                address@hidden
Motorola Labs - Paris                        +33 1 69 35 48 04 (Ph) 
Parc Les Algorithmes, Commune de St Aubin    +33 6 72 01 06 33 (Mob) 
91193 Gif-Sur-Yvette FRANCE                  +33 1 69 35 77 01 (Fax) 

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