Error Bound for Computed Eigenvalues.

We have

$$\chi((\wtd\alpha,\wtd\beta),(\alpha,\beta)) \le\frac {\Vert r\Vert _2}{\gamma(A,B)}$$ (106)

for some eigenvalue $(\alpha,\beta)$ of $\{A,B\}$. To use this bound, we need an estimation to $\gamma(A,B)$. This can be done by first finding $B_{\phi}$ as we mentioned above and then estimating its smallest eigenvalue.