实n维复半空间的Dirichlet积分调和插值拟合：DIDACKS III
Closed-form Dirichlet integral harmonic interpolation-fits for real n-dimensional and complex half-space: DIDACKS III
摘要：
本文给出了一种基于“基本解”的能量范数谐波插值方法，用于两个感兴趣的半空间设置：上半部分$\mathbb{R}^n$平面，其中基本解满足拉普拉斯方程，以及上半部分复平面，其中简单极点是感兴趣的。这种方法可以处理高阶极点拟合，以及对数源拟合，在复杂的设置，它可以处理高阶多极拟合在一般的实$\mathbb{R}^n$设置。在实$\mathbb{R}^n$半空间设置中的高阶多极子特别令人感兴趣，因为基于常用类型的径向基函数（逆多重二次曲面）的拟合可以被重新解释为基于多极子的插值，其最小化能量形式。
英文摘要：
This article gives a ``fundamental solution'' based energy-norm harmonic interpolation approach for two half-space settings of interest: the upper-half $\mathbb{R}^n$ plane, where fundamental solutions satisfy Laplace's equation, and the upper-half complex plane, where simple poles are of interest. This approach can handle higher-order pole fits, as well as logarithmic source fits, in the complex setting and it can handle higher-order multipole fits in the general real $\mathbb{R}^n$ setting. Higher-order multipoles in the real $\mathbb{R}^n$ half-space setting are of particular interest since fits based on a commonly used type of radial-basis function (inverse multiquadrics) can be reinterpreted as multipole based interpolations that minimize energy forms.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
