用广义傅里叶插值分析散乱高维数据
Analysis of scattered higher dimensional data using generalized Fourier interpolation
摘要：
提出了一种基于平方根概率密度正交函数级数插值的高维散乱数据分析方法。该方法的目标是当模型和/或数据仅作为离散事件可用时的用例。虽然快速有效的算法对于伪谱（基于网格节点）方法来说是众所周知的，但这项工作的重点是谱（非基于网格）方法。一个典型的应用是从高能粒子碰撞中探测到的事件中提取物理模型参数。提供了几个例子，并与现有的常规程序的性能进行比较。在某些情况下，该方法可以表现为数据的最佳可观察性，例如接近Cramer-Rao界限的能力。
英文摘要：
A method based on orthogonal function series interpolation of the square root probability density to analyze higher dimensional scattered data is presented. The method is targeted for the use-case when the model and/or data are available only as discrete events. While fast and efficient algorithms are well known for pseudo-spectral (grid node based) methods, this work focuses on a spectral (non grid based) approach. A typical application is the extraction of physics model parameters from events detected in high energy particle collisions. Several examples are provided and the performance is compared to existing conventional procedures. In some cases the method can be shown to behave as an optimal observable of the data, exemplified by the ability to approach the Cramer-Rao bound.
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