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Penn State（宾夕法尼亚州立大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文提出新的80位正权重Gauss-Hermite和Gauss-Legendre求积规则，适用于最多五维，改进或填补了现有规则，并提供多语言软件实现。
AI 中文摘要
本文包含新的80位正权重Gauss-Hermite和正权重内节点Gauss-Legendre求积规则，适用于最多五维以及不同的多项式精度（取决于求积类型和维度）。其中一些规则改进了文献中已有的最佳规则，而另一些则提供了此前（除张量积外）不存在的规则。这些结果是通过将先前研究人员开发的方法与新方法相结合而得到的。完整的精度规则可在https://doi.org/10.5281/zenodo.22881864获取。提供这些规则的软件可通过软件包注册表和/或GitHub获得：Quadriceps.jl（支持64位和128位；https://github.com/NittanyLion/Quadriceps.jl）、quadriceps-py（仅64位；https://github.com/NittanyLion/quadriceps-py）以及quadriceps-r（仅64位；https://github.com/NittanyLion/quadriceps-r）。用于创建这些规则的软件可通过PositiveWeightQuadratureSolvers.jl（https://github.com/NittanyLion/PositiveWeightQuadratureSolvers.jl）获取。复制包位于QuadricepsReplicationPackage.jl（https://github.com/NittanyLion/QuadricepsReplicationPackage.jl）。所有五个软件包的快照已存档于https://doi.org/10.5281/zenodo.22883240。
英文摘要
This paper contains new 80-digit positive-weight Gauss-Hermite and positive-weight interior-node Gauss-Legendre quadrature rules for up to five dimensions and varying polynomial degree accuracy (depending on quadrature type and dimension). Some of these rules improve on the best available rules in the literature and some offer rules where none (other than the tensor product) existed. The results were produced by combining methodology developed by previous researchers with new approaches. The full precision rules themselves are at https://doi.org/10.5281/zenodo.22881864. Software in Julia, Python, and R providing the rules is available via a package registry and/or GitHub: Quadriceps.jl (both 64-bit and 128-bit; https://github.com/NittanyLion/Quadriceps.jl), quadriceps-py (64-bit only; https://github.com/NittanyLion/quadriceps-py), and quadriceps-r (64-bit only; https://github.com/NittanyLion/quadriceps-r). The software used to create these rules is available via PositiveWeightQuadratureSolvers.jl (https://github.com/NittanyLion/PositiveWeightQuadratureSolvers.jl). The replication package is at QuadricepsReplicationPackage.jl (https://github.com/NittanyLion/QuadricepsReplicationPackage.jl). A snapshot of all five packages is archived at https://doi.org/10.5281/zenodo.22883240.
Comments16 pages, 2 figures
