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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