Block structured matrix-sequences and their spectral and singular value canonical distributions: a general theory
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arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866917911844618240 |
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| author | Furci, Isabella Adriani, Andrea Serra-Capizzano, Stefano |
| author_facet | Furci, Isabella Adriani, Andrea Serra-Capizzano, Stefano |
| contents | In recent years more and more involved block structures appeared in the literature in the context of numerical approximations of complex infinite dimensional operators modeling real-world applications. In various settings, thanks the theory of generalized locally Toeplitz matrix-sequences, the asymptotic distributional analysis is well understood, but a general theory is missing when general block structures are involved. The central part of the current work deals with such a delicate generalization when blocks are of (block) unilevel Toeplitz type, starting from a problem of recovery with missing data. Visualizations, numerical tests, and few open problems are presented and critically discussed. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2409_06465 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Block structured matrix-sequences and their spectral and singular value canonical distributions: a general theory Furci, Isabella Adriani, Andrea Serra-Capizzano, Stefano Numerical Analysis 15A18, 34L20, 35P20, 15A69, 15B05 In recent years more and more involved block structures appeared in the literature in the context of numerical approximations of complex infinite dimensional operators modeling real-world applications. In various settings, thanks the theory of generalized locally Toeplitz matrix-sequences, the asymptotic distributional analysis is well understood, but a general theory is missing when general block structures are involved. The central part of the current work deals with such a delicate generalization when blocks are of (block) unilevel Toeplitz type, starting from a problem of recovery with missing data. Visualizations, numerical tests, and few open problems are presented and critically discussed. |
| title | Block structured matrix-sequences and their spectral and singular value canonical distributions: a general theory |
| topic | Numerical Analysis 15A18, 34L20, 35P20, 15A69, 15B05 |
| url | https://arxiv.org/abs/2409.06465 |