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Error Bound for Computed Eigenvectors.
Keep the assignments to
, let
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

(107) 
This bound also needs information on
, besides the residual error and .
Usually such information
is available after a successful computation by,
e.g., the shiftandinvert Lanczos
algorithm which usually delivers eigenvalues in the neighborhood
of a shift and consequently yields good information on the
.
Susan Blackford
20001120