Taylor Numbers for the Fast Multipole Method

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Abstract

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.

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europepmc
last seen: 2026-05-19T01:45:01.086888+00:00