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Error Bound for Computed Eigenvalues.

It can be proved [425] that up to the first order of $\Vert(E,F)\Vert _2$, there is an eigenvalue $(\alpha,\beta)$ of $A$ and $B$ satisfying
\chi((\alpha, \beta),(\wtd\alpha,\wtd\beta))
\simle c_{(\alpha,\beta)} \cdot \Vert(E_2,F_2)\Vert _2,
\end{displaymath} (244)


\equiv\frac {\Vert x\Vert _2\Vert y\Vert...
...\sqrt {\vert y^{\ast} Ax\vert^2 + \vert y^{\ast} Bx\vert^2}}.

It is called the individual condition number of $(\alpha,\beta)$, which in actual computations will be estimated with the exact eigenvectors $x$ and $y$ replaced by their approximations $\wtd x$ and $\wtd y$.

Susan Blackford 2000-11-20