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      Taylor Numbers for the Fast Multipole Method

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            We present a novel linear algebra formulation of the math behind the FastMultipole Method (FMM). For this, we introduce the Taylor numbers. They are polynomials governed by differential algebra but used like integers and floating points. They help simplify the FMM math and potentially any scientific programming project.


            Author and article information

            ScienceOpen Preprints
            28 August 2022
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            Author notes

            This work has been published open access under Creative Commons Attribution License CC BY 4.0 , which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. Conditions, terms of use and publishing policy can be found at www.scienceopen.com .

            All data generated or analysed during this study are included in this published article (and its supplementary information files).
            Data structures & Algorithms,Mathematical & Computational physics,Bioinformatics & Computational biology
            Fast Multipole Method (FMM),Differential Algebra (DA),Polynomial rings,Automatic differentiation,N-body problems,Molecular Dynamics (MD)


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