论文标题
Stahl定理对PT的全态嵌入的含义。 1：理论融合
Implications of Stahl's Theorems to Holomorphic Embedding Pt. 1: Theoretical Convergence
论文作者
论文摘要
在动力工程圈中，已被称为Stahl定理已被用来证明其适用于功率流（PF）问题的全像嵌入方法（HEM）的收敛保证。在这本两部分的论文中，我们更详细地研究了Stahl定理对定理和数值收敛的含义，以解决这些定理现在正在应用的更广泛的问题。在Pt。 1，我们使用必要的数学列表介绍了定理，然后翻译该语言以表明其对一般的非线性问题和PF问题的融合的影响。我们表明，除其他可能性外，嵌入特定的Chebotarev点的存在可能是收敛的理论障碍。在同伴论文中讨论了对融合的数值障碍。
What has become known as Stahl's Theorem in power engineering circles has been used to justify a convergence guarantee of the Holormorphic Embedding Method (HEM) as it applies to the power flow (PF) problem. In this two-part paper, we examine in more detail the implications of Stahl's theorems to both theoretcial and numerical convergence for a wider range of problems to which these theorems are now being applied. In Pt. 1, we introduce the theorem using the necessary mathematical parlance and then translate the language to show its implications to convergence of nonlinear problems in general and the PF problem specifically. We show that among other possibilities the existence of the Chebotarev points, which are embedding specific, are a possible theoretical impediment to convergence. Numerical impediments to convergences are discussed in the companion paper.
