%0 Journal Article 
%A Cobos Sánchez, Clemente
%A García Pacheco, Francisco Javier
%A Moreno Pulido, Soledad
%A Sáez Martínez, Sol
%T Supporting vectors of continuous linear operators
%D 2017
%@ 2008-8752
%U http://hdl.handle.net/10498/36561
%X The set of supporting vectors of a continuous linear operator, that
is, the normalized vectors at which the operator attains its norm, is decomposed
into its convex components. In the complex case, the set of supporting vectors
of a nonzero functional is proved to be path-connected. We also introduce
the concept of generalized supporting vectors for a sequence of operators as
the normalized vectors that maximize the summation of the squared norm of
those operators. We determine the set of generalized supporting vectors for
the particular case of a finite sequence of real matrices. Finally, we unveil the
relation between the supporting vectors of a real matrix A and the Tikhonov
regularization minx∈Rn kAx − bk + αkxk reaching the conclusion that, by an
appropriate choice of b and α, the supporting vectors of A can be obtained via
solving the Tikhonov regularization minx∈Rn kAx − bk + αkxk.
%K supporting vector
%K matrix norm
%K Tikhonov regularization
%~ Universidad de Cádiz