Comparison of Numerical Solvers for Differential Equations for Holonomic Gradient Method in Statistics

[2111.10947] Comparison of Numerical Solvers for Differential Equations for Holonomic Gradient Method in Statistics Skip to main content Search Submit Donate Log in Search arXiv Press Enter to search · Advanced search Mathematics > Numerical Analysis arXiv:2111.10947 (math) [Submitted on 22 Nov 2021 ( v1 ), last revised 9 Apr 2026 (this version, v3)] Title: Comparison of Numerical Solvers for Differential Equations for Holonomic Gradient Method in Statistics Authors: Nobuki Takayama , Takaharu Yaguchi , Yi Zhang View a PDF of the paper titled Comparison of Numerical Solvers for Differential Equations for Holonomic Gradient Method in Statistics, by Nobuki Takayama and 2 other authors View PDF HTML (experimental) Abstract: Definite integrals with parameters of holonomic functions satisfy holonomic systems of linear partial differential equations. When we restrict parameters to a one dimensional curve, the system becomes a linear ordinary differential equation (ODE) with respect to a curve in the parameter space. We can evaluate the integral by solving the linear ODE numerically. This approach to evaluate numerically definite integrals is called the holonomic gradient method (HGM) and it is useful to evaluate several normalizing constants in statistics. We will discuss and compare methods to solve linear ODE's to evaluate normalizing constants. Comments: 24 pages Subjects: Numerical Analysis (math.NA) ; Computation (stat.CO) MSC classes: 62-8, 62E17, 65L04 Cite as: arXiv:2111.10947 [math.NA] (or arXiv:2111.10947v3 [math.NA] for this version) https://doi.org/10.48550/arXiv.2111.10947 Focus to learn more arXiv-issued DOI via DataCite Submission history From: Nobuki Takayama [ view email ] [v1] Mon, 22 Nov 2021 02:13:52 UTC (306 KB) [v2] Tue, 15 Aug 2023 02:32:56 UTC (629 KB) [v3] Thu, 9 Apr 2026 07:40:27 UTC (419 KB) Full-text links: Access Paper: View a PDF of the paper titled Comparison of Numerical Solvers for Differential Equations for Holonomic Gradient Method in Statistics, by Nobuki Takayama and 2 other authors View PDF HTML (experimental) TeX Source view license Current browse context: math.NA < prev | next > new | recent | 2021-11 Change to browse by: cs cs.NA math stat stat.CO 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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