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Residual Vector.

Let
denote a computed eigenvalue, and let
be its corresponding computed eigenvector.
For the simplicity,
we normalize the computed eigenvector and eigenvalue so that

The corresponding *residual vector* or
*residual error* is defined by

Ideally, we would like to have , but in practice is small.
It is conceivable that a small residual error implies
good accuracy in the computed
and .
We are interested in knowing how accurate the computed
and are, given .

Susan Blackford
2000-11-20