Row-Local Spectral Certificates and Analog Courant Metrics for Finite-Bandwidth Feedback-Coupled Solvers

[2607.27609] Row-Local Spectral Certificates and Analog Courant Metrics for Finite-Bandwidth Feedback-Coupled Solvers Skip to main content Search Submit Donate Log in Search arXiv Press Enter to search · Advanced search Computer Science > Hardware Architecture arXiv:2607.27609 (cs) [Submitted on 30 Jul 2026 ( v1 ), last revised 14 Aug 2026 (this version, v2)] Title: Row-Local Spectral Certificates and Analog Courant Metrics for Finite-Bandwidth Feedback-Coupled Solvers Authors: Arash Ghasemi View a PDF of the paper titled Row-Local Spectral Certificates and Analog Courant Metrics for Finite-Bandwidth Feedback-Coupled Solvers, by Arash Ghasemi View PDF HTML (experimental) Abstract: This paper identifies a dynamical constraint on analog-computing approaches in which a row of the matrix is represented by an impedance network. It shows that the fastest normalized mode is no more than 2$\pi$ times the largest combined unity-gain bandwidth (CUGBW) among all the circuit rows. The CUGBW of a row equals its finite-gain-adjusted unity-gain bandwidth plus the contributions of all rows coupled to it. Each contribution is the square root of the product of the two rows' unity-gain bandwidths multiplied by their coupling conductance and divided by the square root of the product of their total conductance loadings. This bound plays a role analogous to the Courant-number restriction in time-stepping methods by limiting the operator rates that analog hardware can physically represent and resolve at its outputs. It is shown that in mixed-signal approach, the Courant metrics become stability criteria, and they must be less than 2 in order for the solver to remain stable. The theory is validated using large-scale LTspice simulations across architectures ranging from CMOS to thermionic vacuum-tube circuits. The benchmark circuits implement a one-dimensional heat equation, a graph-based semi-supervised learning problem, and a graph-regularized regression. Comments: Revised Version of the Original Manuscript Subjects: Hardware Architecture (cs.AR) Cite as: arXiv:2607.27609 [cs.AR] (or arXiv:2607.27609v2 [cs.AR] for this version) https://doi.org/10.48550/arXiv.2607.27609 Focus to learn more arXiv-issued DOI via DataCite Submission history From: Arash Ghasemi [ view email ] [v1] Thu, 30 Jul 2026 02:54:59 UTC (4,483 KB) [v2] Fri, 14 Aug 2026 18:21:01 UTC (3,821 KB) Full-text links: Access Paper: View a PDF of the paper titled Row-Local Spectral Certificates and Analog Courant Metrics for Finite-Bandwidth Feedback-Coupled Solvers, by Arash Ghasemi View PDF HTML (experimental) TeX Source view license Current browse context: cs.AR < prev | next > new | recent | 2026-07 Change to browse by: cs References & Citations NASA ADS Google Scholar Semantic Scholar export BibTeX citation Loading... BibTeX formatted citation × loading... Data provided by: Bookmark Bibliographic Tools Bibliographic and Citation Tools Bibliographic Explorer Toggle Bibliographic Explorer ( What is the Explorer? ) Connected Papers Toggle Connected Papers ( What is Connected Papers? ) Litmaps Toggle Litmaps ( What is Litmaps? ) scite.ai Toggle scite Smart Citations ( What are Smart Citations? ) Code, Data, Media Code, Data and Media Associated with this Article alphaXiv Toggle alphaXiv ( What is alphaXiv? ) Links to Code Toggle CatalyzeX Code Finder for Papers ( What is CatalyzeX? ) DagsHub Toggle DagsHub ( What is DagsHub? ) GotitPub Toggle Gotit.pub ( What is GotitPub? ) Huggingface Toggle Hugging Face ( What is Huggingface? ) ScienceCast Toggle ScienceCast ( What is ScienceCast? ) Demos Demos Replicate Toggle Replicate ( What is Replicate? ) Spaces Toggle Hugging Face Spaces ( What is Spaces? ) Spaces Toggle TXYZ.AI ( What is TXYZ.AI? ) Related Papers Recommenders and Search Tools Link to Influence Flower Influence Flower ( What are Influence Flowers? ) Core recommender toggle CORE Recommender ( What is CORE? ) Author Venue Institution Topic About arXivLabs arXivLabs: experimental projects with community collaborators arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website. Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them. Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs . Which authors of this paper are endorsers? | Disable MathJax ( What is MathJax? ) We gratefully acknowledge support from our major funders , member institutions , , and all contributors. About · Help · Contact · Subscribe · Copyright · Privacy · Accessibility · Operational Status (opens in new tab) Major funding support from

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