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Figure 5.9 Saddle-maximum hypercrest projection and its evolution for two different TLS
solutions (minima) in the two-dimensional TLS hyperplane.
the upper part until the top part, given by the asymptote. Figure 5.11 shows
the corresponding weight vector evolution by means of the blue lines. All the
trajectories, beginning from the green points, go to the straight line through the
minimum and the saddle (TLS projection of the saddle-minimum hypervalley) at
the right side of the saddle and then converge to the minimum. All the trajectories
beginning from the red points go to the same straight line at the left side of the
saddle and then diverge in the direction of the straight line.
5.3.11 GeTLS Domain of Convergence
The GeTLS domain of convergence is similar to the TLS domain of convergence
(i.e., it is bordered by the same barriers and asymptotes and the same maximum
locus tangent). The following remark explains the differences.
Remark 115 (GTLS Characterization) Unlike the TLS problem, which can
be extended to a higher-dimensional problem just to exploit the MCA, the GeTLS
problem can be studied and solved only without a change in dimensionality
because its formulation [ eq. ( 5.6 )] does not have a corresponding Rayleigh
quotient.
As a consequence, the MCA stability analysis cannot be applied. Then there
are no hypercrest projections and the saddle cones are the volumes of attraction
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