Análisis de aplicaciones de mejor aproximación en espacios de Hilbert
| dc.contributor.advisor | Ramos Fernández, Julio César | |
| dc.contributor.author | Vargas Ruiz, Aura Yorleny | |
| dc.contributor.author | Guerrero Guio, John Alejandro | |
| dc.date.accessioned | 2025-08-05T15:15:30Z | |
| dc.date.available | 2025-08-05T15:15:30Z | |
| dc.date.created | 2025-07-02 | |
| dc.description | Este trabajo explora las aplicaciones de mejor aproximación (BAM) en espacios de Hilbert, partiendo de nociones básicas hasta llegar a definiciones más recientes. Se toma como referencia principal el artículo Best Approximation Mappings in Hilbert Spaces de Bauschke, Ouyang y Wang (2020), donde se introduce una caracterización general de este tipo de aplicaciones. A lo largo del documento se incluyen ejemplos y resultados que muestran cómo estas aplicaciones permiten abordar problemas de aproximación desde una perspectiva más amplia. | |
| dc.description.abstract | This work explores the Best Approximation Mappings (BAM) in Hilbert spaces, starting from basic notions and progressing to more recent definitions. The main reference is the article Best Approximation Mappings in Hilbert Spaces by Bauschke, Ouyang, and Wang (2020), which introduces a general characterization of this type of mapping. Throughout the document, examples and results are included to illustrate how these mappings enable a broader approach to approximation problems. | |
| dc.format.mimetype | ||
| dc.identifier.uri | http://hdl.handle.net/11349/98377 | |
| dc.language.iso | spa | |
| dc.publisher | Universidad Distrital Francisco José de Caldas | |
| dc.relation.references | H. H. Bauschke, P. L. Combettes, H. H. Bauschke, and P. L. Combettes. Convex analysis and monotone operator theory in Hilbert spaces, Second Edition. Springer, 2017. | |
| dc.relation.references | H. H. Bauschke, D. Noll, and H. M. Phan. Linear and strong convergence of algorithms involving averaged nonexpansive operators. Journal of Mathematical Analysis and Applications, 421(1):1–20, 2015 | |
| dc.relation.references | H. H. Bauschke, H. Ouyang, and X. Wang. On circumcenter mappings induced by nonexpansive operators. arXiv preprint arXiv:1811.11420, 2018. | |
| dc.relation.references | H. H. Bauschke, H. Ouyang, and X. Wang. Best approximation mappings in hilbert spaces. Mathematical Programming, 195(1):855–901, 2022. | |
| dc.relation.references | R. Behling, J.-Y. Bello-Cruz, and L.-R. Santos. The block-wise circumcentered–reflection method. Computational Optimization and Applications, 76(3):675–699, 2020. | |
| dc.relation.references | P. Blanchard and E. Brüning. Mathematical methods in Physics: Distributions, Hilbert space operators, variational methods, and applications in quantum physics, volume 69. Birkhäuser, 2015. | |
| dc.relation.references | P. L. Combettes and I. Yamada. Compositions and convex combinations of averaged nonexpansive operators. Journal of Mathematical Analysis and Applications, 425(1):55–70, 2015. | |
| dc.relation.references | F. Deutsch and F. Deutsch. Best approximation in inner product spaces, volume 7. Springer, 2001. | |
| dc.relation.references | E. Kreyszig. Introductory functional analysis with applications, volume 17. John Wiley & Sons, 1991. | |
| dc.relation.references | C. D. Meyer. Matrix Analysis and Applied Linear Algebra. Society for Industrial and Applied Mathematics, 2023. | |
| dc.relation.references | J. Munkres. Topology james munkres second edition. | |
| dc.relation.references | R. Rockafellar. Convex analysis. Princeton Mathematical Series, 28, 1997. | |
| dc.rights.acceso | Abierto (Texto Completo) | |
| dc.rights.accessrights | OpenAccess | |
| dc.subject | Mejor aproximación | |
| dc.subject | Espacios de Hilbert | |
| dc.subject | BAM | |
| dc.subject | Convergencia | |
| dc.subject.keyword | Best approximation | |
| dc.subject.keyword | Hilbert spaces | |
| dc.subject.keyword | BAM | |
| dc.subject.lemb | Matemáticas -- Tesis y disertaciones académicas | |
| dc.title | Análisis de aplicaciones de mejor aproximación en espacios de Hilbert | |
| dc.title.titleenglish | Analysis of Best Approximation Mappings in Hilbert Spaces | |
| dc.type | bachelorThesis | |
| dc.type.coar | http://purl.org/coar/resource_type/c_7a1f | |
| dc.type.degree | Monografía | |
| dc.type.driver | info:eu-repo/semantics/bachelorThesis |
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