History of confluent Vandermonde matrices and inverting them algorithms

[2407.15696] History of confluent Vandermonde matrices and inverting them algorithms Skip to main content Search Submit Donate Log in Search arXiv Press Enter to search · Advanced search Mathematics > History and Overview arXiv:2407.15696 (math) [Submitted on 22 Jul 2024 ( v1 ), last revised 8 Apr 2026 (this version, v2)] Title: History of confluent Vandermonde matrices and inverting them algorithms Authors: Jerzy S Respondek View a PDF of the paper titled History of confluent Vandermonde matrices and inverting them algorithms, by Jerzy S Respondek View PDF Abstract: The author was encouraged to write this review by numerous enquiries from researchers all over the world, who needed a ready-to-use algorithm for the inversion of confluent Vandermonde matrices which works in quadratic time for any values of the parameters allowed by the definition, including the case of large root multiplicities of the characteristic polynomial. Article gives the history of the title special matrix since 1891 and surveys algorithms for solving linear systems with the title class matrix and inverting it. In particular, it presents, also by example, a numerical algorithm which does not use symbolic computations and is ready to be implemented in a general-purpose programming language or in a specific mathematical package. Subjects: History and Overview (math.HO) MSC classes: 15-03, 65F05, 15B99 Cite as: arXiv:2407.15696 [math.HO] (or arXiv:2407.15696v2 [math.HO] for this version) https://doi.org/10.48550/arXiv.2407.15696 Focus to learn more arXiv-issued DOI via DataCite Submission history From: Jerzy Respondek [ view email ] [v1] Mon, 22 Jul 2024 15:01:48 UTC (948 KB) [v2] Wed, 8 Apr 2026 23:31:41 UTC (991 KB) Full-text links: Access Paper: View a PDF of the paper titled History of confluent Vandermonde matrices and inverting them algorithms, by Jerzy S Respondek View PDF view license Current browse context: math.HO < prev | next > new | recent | 2024-07 Change to browse by: math 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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