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Zhurnal Vychislitel'noi Matematiki i Matematicheskoi Fiziki, 2024, Volume 64, Number 4, paper published in the English version journal (Mi zvmmf11735)  

Papers published in the English version of the journal

Numerical range and a generalization of Duffin’s overdamping criterion

R. Hildebrandab

a Moscow Institute of Physics and Technology (National Research University), 141701, Dolgoprudny, Moscow oblast, Russia
b Skoltech, 121205, Moscow, Russia
Abstract: The joint numerical range of tuples of matrices is a powerful tool for proving results which are useful in optimization, such as the $\mathcal{S}$-lemma. Here we provide a similar proof for another result, namely the equivalence of a certain positivity criterion to Duffin’s overdamping condition involving quadratic matrix-valued polynomials. We show how the proof is generalizable to higher degrees of matrix-valued polynomials.
Key words: joint numerical range, overdamping condition, convexity.
Received: 06.10.2023
Revised: 20.11.2023
Accepted: 07.06.2024
English version:
Computational Mathematics and Mathematical Physics, 2024, Volume 64, Issue 4, Pages 599–604
DOI: https://doi.org/10.1134/S0965542524700015
Document Type: Article
Language: English
Citation: R. Hildebrand, “Numerical range and a generalization of Duffin’s overdamping criterion”, Comput. Math. Math. Phys., 64:4 (2024), 599–604
Citation in format AMSBIB
\Bibitem{Hil24}
\by R.~Hildebrand
\paper Numerical range and a generalization of Duffin’s overdamping criterion
\jour Comput. Math. Math. Phys.
\yr 2024
\vol 64
\issue 4
\pages 599--604
\mathnet{http://mi.mathnet.ru/zvmmf11735}
\crossref{https://doi.org/10.1134/S0965542524700015}
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