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The stopping criterion is
determined by the user through specification of the
parameter `tol`.
The default value for `tol` is machine precision
There are several things to consider when setting this parameter.
In absence of all other considerations, one should expect a
computed eigenvalue to satisfy

where is the eigenvalue of nearest to
Typically, decreasing the value of `tol`
will increase the work required to satisfy the stopping criterion. However,
setting `tol` too large may cause eigenvalues
to be missed when they are multiple or very tightly clustered.
Typically, a fairly small setting of `tol` and a reasonably large
setting of `ncv` is required to avoid missing multiple eigenvalues.
However, some care must be taken. It is possible to set `tol` so small
that convergence never occurs. There may be additional complications when the
matrix is non-normal or when the eigenvalues of interest are clustered
near the origin. A detailed discussion of the stopping rules and what
they imply about the computed results is given in
Chapter 4 § 4.6.

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*Chao Yang*

*11/7/1997*