RT journal article
T1 Supporting vectors of continuous linear operators
A1 Cobos Sánchez, Clemente
A1 García Pacheco, Francisco Javier
A1 Moreno Pulido, Soledad
A1 Sáez Martínez, Sol
A2 Ingeniería en AutomáticaElectrónica, Arquitectura y Redes de Computadores
A2 Matemáticas
K1 supporting vector
K1 matrix norm
K1 Tikhonov regularization
AB The set of supporting vectors of a continuous linear operator, thatis, the normalized vectors at which the operator attains its norm, is decomposedinto its convex components. In the complex case, the set of supporting vectorsof a nonzero functional is proved to be path-connected. We also introducethe concept of generalized supporting vectors for a sequence of operators asthe normalized vectors that maximize the summation of the squared norm ofthose operators. We determine the set of generalized supporting vectors forthe particular case of a finite sequence of real matrices. Finally, we unveil therelation between the supporting vectors of a real matrix A and the Tikhonovregularization minx∈Rn kAx − bk + αkxk reaching the conclusion that, by anappropriate choice of b and α, the supporting vectors of A can be obtained viasolving the Tikhonov regularization minx∈Rn kAx − bk + αkxk.
PB Duke University Press
SN 2008-8752
YR 2017
FD 2017
LK http://hdl.handle.net/10498/36561
UL http://hdl.handle.net/10498/36561
LA eng
DS Repositorio Institucional de la Universidad de Cádiz
RD 10-nov-2026