Editing Inverse iteration (section)

=== Estimates based on statistics ===

In some real-time applications one needs to find  eigenvectors  for matrices with  a speed of millions of matrices per second. In such applications, typically the statistics of matrices is known in advance and one can take as an approximate eigenvalue the average eigenvalue for some large matrix sample.
Better, one may calculate the mean ratio of the eigenvalues to the trace or the norm of the  matrix and estimate the average eigenvalue as the trace or norm multiplied by the average value of that ratio.  Clearly such a method can be used only with discretion and only when high precision is not critical. 
This approach of estimating an average eigenvalue can be combined with other methods to avoid excessively large error.