论文标题
delaVallée-Poussin和sums sums sums sums的核心和依赖的金斯总和
A kernel-independent sum-of-Gaussians method by de la Vallée-Poussin sums
论文作者
论文摘要
在科学和工程计算的许多应用中，经常需要通过高斯人（SOG）进行相互作用的内核近似，以构建用于内核求和或卷积问题的有效算法。在本文中，我们通过引入delaVallée-Poussin和Chebyshev多项式提出了一种独立于内核的SOG方法。 SOG适用于一般相互作用的内核，高斯带宽的下限是可调的，因此可以通过快速高斯算法很容易地将高斯概括。基于平衡的截断基于平衡的截断，可以通过模型减少来进一步减少高斯人的数量。关于准确性和模型降低效率的数值结果显示了所提出方法的有吸引力的性能。
Approximation of interacting kernels by sum of Gaussians (SOG) is frequently required in many applications of scientific and engineering computing in order to construct efficient algorithms for kernel summation or convolution problems. In this paper, we propose a kernel-independent SOG method by introducing the de la Vallée-Poussin sum and Chebyshev polynomials. The SOG works for general interacting kernels and the lower bound of Gaussian bandwidths is tunable and thus the Gaussians can be easily summed by fast Gaussian algorithms. The number of Gaussians can be further reduced via the model reduction based on the balanced truncation based on the square root method. Numerical results on the accuracy and model reduction efficiency show attractive performance of the proposed method.
