Academic Journal
Supporting vectors of continuous linear operators
| العنوان: | Supporting vectors of continuous linear operators |
|---|---|
| المؤلفون: | Cobos-Sánchez, Clemente, García-Pacheco, Francisco Javier, Moreno-Pulido, Soledad, Sáez-Martínez, Sol |
| بيانات النشر: | Duke University Press |
| سنة النشر: | 2017 |
| المجموعة: | Project Euclid (Cornell University Library) |
| مصطلحات موضوعية: | supporting vector, matrix norm, Tikhonov regularization, 15A18, 15A60, 47L25 |
| الوصف: | 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 $\min_{x\in\mathbb{R}^{n}}\Vert Ax-b\Vert +\alpha \Vert x\Vert $ reaching the conclusion that, by an appropriate choice of $b$ and $\alpha$ , the supporting vectors of $A$ can be obtained via solving the Tikhonov regularization $\min_{x\in\mathbb{R}^{n}}\Vert Ax-b\Vert +\alpha \Vert x\Vert $ . |
| نوع الوثيقة: | text |
| وصف الملف: | application/pdf |
| اللغة: | English |
| تدمد: | 2008-8752 |
| Relation: | https://projecteuclid.org/euclid.afa/1498723219; Ann. Funct. Anal. 8, no. 4 (2017), 520-530 |
| DOI: | 10.1215/20088752-2017-0016 |
| الاتاحة: | https://projecteuclid.org/euclid.afa/1498723219 https://doi.org/10.1215/20088752-2017-0016 |
| Rights: | Copyright 2017 Tusi Mathematical Research Group |
| رقم الانضمام: | edsbas.FBF196EA |
| قاعدة البيانات: | BASE |
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