Re: Good eigenvalue/eigenvector test problems for eigs?

[Sebastien Loisel]

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

This should not be ill conditioned. A-2I is diagonally dominant and symmetric so all its eigenvalues are positive. 6I-A is also diagonally dominant and symmetric so its eigenvalues are all positive. As a result, the eigenvalues of A are between 2 and 6, this is a pretty tight bound. The condition number is uniformly bounded by 3.

Sebastien Loisel