论文标题
用于实验数据的稳定的高阶群组公式
Stable high-order cubature formulas for experimental data
论文作者
论文摘要
在许多应用中，获取数据以适合已知的立方体公式（CF）是不切实际的（甚至不是不可能）。取而代之的是，经常在等距甚至分散的位置获取实验数据。在这项工作中，为此目的而开发了稳定的高阶CFS（在非负数的意义上）。这些是基于允许数据点n数量n的数量大于基本函数k的数量k的方法。这产生了（N-K）维仿生线性子空间，从中选择了立方体权重，以最大程度地减少与CF稳定性相对应的某些规范。在此过程中，提出并仔细研究了两种新型的稳定高阶CF。
In many applications, it is impractical -- if not even impossible -- to obtain data to fit a known cubature formula (CF). Instead, experimental data is often acquired at equidistant or even scattered locations. In this work, stable (in the sense of nonnegative only cubature weights) high-order CFs are developed for this purpose. These are based on the approach to allow the number of data points N to be larger than the number of basis functions K which are integrated exactly by the CF. This yields an (N-K)-dimensional affine linear subspace from which cubature weights are selected that minimize certain norms corresponding to stability of the CF. In the process, two novel classes of stable high-order CFs are proposed and carefully investigated.
