Re: Proof of (8.21)

 
Dear Magnus Jansson,

The point of the proof of (8.21) is to show that there exists a \Delta_I
such that l_O is equal to the upper bound w_I * gamma(G).

You are right, the tilde variables denote the SVD of G^{-1}, and the
proof shows clearly that a particular choise of \Delta_I does
indeed yield the upper bound. To see this let S denote the matrix of
singular values. Then the matrix S tilde{S} has as its first element
sigma(G)*sigma(G^-1) = gamma(G).

Note that the SVD of G^{-1} is not really equal to VS^{-1}U^H,
because the order of the singular values and vectors is reversed. This
was the reason for introducing the tilde notation.

Best regards,
Sigurd Skogestad
Received on Thu Feb 27 14:24:18 1997