Additive Stability of Frames
Fuente:
arXiv
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| Auteurs principaux: | , , |
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| Format: | Preprint |
| Publié: |
2023
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| _version_ | 1866912436995489792 |
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| author | Asipchuk, Oleg Glidewell, Jacob Rodriguez, Luis |
| author_facet | Asipchuk, Oleg Glidewell, Jacob Rodriguez, Luis |
| contents | Given a frame in a finite dimensional Hilbert space we construct additive perturbations which decrease the condition number of the frame. By iterating this perturbation, we introduce an algorithm that produces a tight frame in a finite number of steps. Additionally, we give sharp bounds on additive perturbations which preserve frames and we study the effect of appending and erasing vectors to a given tight frame. We also discuss under which conditions our finite-dimensional results are extendable to infinite-dimensional Hilbert spaces. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2309_06331 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Additive Stability of Frames Asipchuk, Oleg Glidewell, Jacob Rodriguez, Luis Functional Analysis 42C15 Given a frame in a finite dimensional Hilbert space we construct additive perturbations which decrease the condition number of the frame. By iterating this perturbation, we introduce an algorithm that produces a tight frame in a finite number of steps. Additionally, we give sharp bounds on additive perturbations which preserve frames and we study the effect of appending and erasing vectors to a given tight frame. We also discuss under which conditions our finite-dimensional results are extendable to infinite-dimensional Hilbert spaces. |
| title | Additive Stability of Frames |
| topic | Functional Analysis 42C15 |
| url | https://arxiv.org/abs/2309.06331 |