Stopping Criterion

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 ${\bf A}$ 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 ${\bf A}$ 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.