LinApart: optimizing the univariate partial fraction decomposition
Bakar Chargeishvili, Levente Fek\'esh\'azy, G\'abor Somogyi, Sam Van, Thurenhout
TL;DR
LinApart is a new algorithm that significantly speeds up univariate partial fraction decomposition for large symbolic expressions by using a closed-form formula, with implementations in Mathematica and C.
Contribution
The paper introduces LinApart, a novel routine that improves efficiency of univariate partial fraction decomposition using a closed-form solution, outperforming existing tools.
Findings
Substantial performance improvements over Mathematica's Apart command
Effective handling of large symbolic expressions
Open-source implementations available
Abstract
We present LinApart, a routine designed for efficiently performing the univariate partial fraction decomposition of large symbolic expressions. Our method is based on an explicit closed formula for the decomposition of rational functions with fully factorized denominators. We provide implementations in both the Wolfram Mathematica and C languages, made available at https://github.com/fekeshazy/LinApart . The routine can provide very significant performance gains over available tools such as the Apart command in Mathematica.
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Taxonomy
TopicsNumerical Methods and Algorithms · Digital Filter Design and Implementation