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About the choice of $ \tilde{s}$

The choice of $ \tilde{s}$ is never bad because it achieves the property

$\displaystyle \vert \tilde{s}^T H \tilde{s} \vert \geq \frac{1}{2} \frac{1}{\sqrt{n}} \sigma(H) \rho^2$ (5.10)

The proof will be skipped.
Frank Vanden Berghen 2004-04-19