讲座题目：A hierarchical random compression method for kernel matrices

主 讲 人：陈端博士

讲座时间：2018年 6月14日15：00-16：00

讲座地点：理学院201报告厅

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理学院

2018年06月13日

讲座内容简介：In this work, we propose a hierarchical random compression method (HRCM) for kernel matrices in fast kernel summations. The HRCM combines the hierarchical framework of the H-matrix and a randomized sampling technique of column and row spaces for far-field interaction kernel matrices. We show that a uniform column/row sampling of a far-field kernel matrix, thus without the need and associated cost to pre-compute a costly sampling distribution, will give a low-rank compression of such low-rank matrices, independent of the matrix sizes and only dependent on the separation of the source and target locations. This far-field random compression technique is then implemented at each level of the hierarchical decomposition for general kernel matrices, resulting in an O(Nlog N) random compression method. Error and complexity analysis for the HRCM are included. Numerical results for electrostatic and Helmholtz wave kernels have validated the efficiency and accuracy of the proposed method with a cross-over matrix size, in comparison of direct O(N^2) summations, in the order of thousands for a 3-4 digits relative accuracy for electrostatic and low frequency wave interaction kernels.

报告人简介：陈端博士，北卡罗莱纳大学夏洛特分校数学与统计系副教授，主要研究方向包括计算数学、计算生物等， 计算生物领域10多个国际期刊的审稿人，已发表学术论文20多篇，受邀报告近10个，主持包括NSF基金资助的多个科研项目。