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Keep the assignments to
be the eigenvector of corresponding to
and let be the smallest distance in chordal metric between
and all the other eigenvalues
of the pair. Then we have
Error Bound for Computed Eigenvectors.
This bound also needs information on
, besides the residual error and .
Usually such information
is available after a successful computation by,
e.g., the shift-and-invert Lanczos
algorithm which usually delivers eigenvalues in the neighborhood
of a shift and consequently yields good information on the