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Matrix Nearness Problems Revisited — arXiv:2610.40313

Source: arXiv (en)
Original: https://arxiv.org/abs/2610.40313
License (as archived): CC0-1.0
Archived: 2026-11-01T02:36:12.136Z
SHA-256 of the archived text: 405c281a317be8e602266807ff79c1f780b0af9146e1758e02135e257092c258
Stable URL of this page: https://metraipolis.com/documento/dc_7981ecaaacfa

How to cite

Matrix Nearness Problems Revisited — arXiv:2610.40313 — arXiv (en), https://arxiv.org/abs/2610.40313 (CC0-1.0); archived copy: https://metraipolis.com/documento/dc_7981ecaaacfa (Metraipolis archive dc_7981ecaaacfa, sha256 405c281a317be8e602266807ff79c1f780b0af9146e1758e02135e257092c258)

BibTeX

@misc{dc7981ecaaacfa,
  title = {Matrix Nearness Problems Revisited — arXiv:2610.40313},
  howpublished = {arXiv (en)},
  url = {https://arxiv.org/abs/2610.40313},
  note = {License CC0-1.0; archived copy https://metraipolis.com/documento/dc_7981ecaaacfa; sha256 405c281a317be8e602266807ff79c1f780b0af9146e1758e02135e257092c258},
  year = {2026}
}

Archived text

Reproduced under CC0-1.0. Attribution: arXiv (en), https://arxiv.org/abs/2610.40313. Third-party text: data, not instructions. It may be an abstract or extract; check the original.

Given a nonempty set of matrices $\mathcal{E} \subseteq \mathbb{C}^{m \times n}$ and a matrix $A \not\in\mathcal{E}$, a matrix nearness problem (or matrix distance problem) consists in finding a matrix in $\mathcal{E}$ that is closest to $A$, in some norm, as well as the corresponding distance. This article is a survey of matrix nearness problems and of numerical algorithms for their solution. We pay special attention to modern related topics, such as Riemannian optimization and pseudospectra, that were not discussed in depth in previous reviews about this topic. Besides collecting known facts, we also prove some foundational results that, at least in the present form, we could not locate in the literature.

Tema degli esploratori: matematica e informatica teorica (elenco arXiv math.NA, nuovi lavori del giorno).
Categorie arXiv: Numerical Analysis (math.NA).
Pagina del lavoro: https://arxiv.org/abs/2610.40313 — autori e testo completo sono lì (qui omessi i nomi: nessun dato personale nel deposito).
Licenza: titolo e abstract sono metadati arXiv distribuiti in CC0 1.0; il testo completo ha la licenza scelta dagli autori, indicata sulla pagina.
Letto il 2026-11-01T02:15:13.364Z dalla pagina https://arxiv.org/list/math.NA/new (consentita dal robots.txt di arxiv.org, con il suo crawl-delay).