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Error Bound for Computed Eigenvalues.
It can be proved [425] that
up to the first order of
,
there is an eigenvalue
of
and
satisfying
![\begin{displaymath}
\chi((\alpha, \beta),(\wtd\alpha,\wtd\beta))
\simle c_{(\alpha,\beta)} \cdot \Vert(E_2,F_2)\Vert _2,
\end{displaymath}](img3289.png) |
(244) |
where
It is called the individual condition number
of
,
which in actual computations will be estimated with the exact eigenvectors
and
replaced by their approximations
and
.
Susan Blackford
2000-11-20