AI 中文总结
该研究提出一种基于帕德序列的算法，将弗罗萨尔特双极点作为诊断对象，可从含不确定性的有限数据中重构解析结构，区分真实特征与虚假结构，已通过多种函数和数据集验证，代码存于GitLab。
AI 中文摘要
从有限数据集中重构函数的解析结构是理论、数值和实验物理学领域的基础问题。尽管帕德近似提供了自然框架，但有限信息效应以及统计和系统不确定性可能会掩盖潜在的解析结构，限制重构的可靠性。本研究将弗罗萨尔特双极点的出现重新解读为不仅是数值伪影，还是携带输入数据解析一致性信息的诊断对象。据此，我们开发了一种通用的基于帕德的算法，该算法利用弗罗萨尔特双极点沿帕德序列的动力学来识别局部不一致性，并迭代重构与数据最兼容的解析结构。该方法无需对不一致性的来源建模，可区分真实解析特征与有限信息效应诱导的虚假结构。我们通过斯蒂尔杰斯函数、具有统计和系统不确定性的真实伪实验数据集以及一般全纯函数对其进行了验证。完整算法作为补充的Mathematica笔记本，存放在开放的GitLab代码库中。
英文摘要
Reconstructing the analytic structure of a function from finite datasets is a fundamental problem across theoretical, numerical, and experimental physics. While Padé approximants provide a natural framework, finite-information effects, as well as statistical and systematic uncertainties, may obscure the underlying analytic structure and limit reconstruction reliability. In this work, we reinterpret the appearance of Froissart doublets not merely as numerical artifacts but as \textit{diagnostic objects} carrying information about the analytic consistency of the input data. Accordingly, we develop a general Padé-based algorithm that exploits the dynamics of Froissart doublets along Padé sequences to identify localized inconsistencies and iteratively reconstruct the analytic structure most compatible with the data. The method requires no model for the origin of the inconsistencies and distinguishes genuine analytic features from spurious structures induced by finite-information effects. We validate it using Stieltjes functions, realistic pseudo-experimental datasets with statistical and systematic uncertainties, and general holomorphic functions. The complete algorithm is provided as a supplementary Mathematica notebook in an open GitLab repository.
Comments25 pages, 7 figures
