Accelerating large partial EVD/SVD calculations by filtered block Davidson methods

doi:10.1007/s11425-016-0274-0

	Accelerating large partial EVD/SVD calculations by filtered block Davidson methods
	Zhou Yunkai 1; Wang Zheng 1; Zhou Aihui2
	2016-08-01
发表期刊	SCIENCE CHINA-MATHEMATICS
ISSN	1674-7283
卷号	59 期号:8 页码:1635-1662
摘要	Partial eigenvalue decomposition (PEVD) and partial singular value decomposition (PSVD) of large sparse matrices are of fundamental importance in a wide range of applications, including latent semantic indexing, spectral clustering, and kernel methods for machine learning. The more challenging problems are when a large number of eigenpairs or singular triplets need to be computed. We develop practical and efficient algorithms for these challenging problems. Our algorithms are based on a filter-accelerated block Davidson method. Two types of filters are utilized, one is Chebyshev polynomial filtering, the other is rational-function filtering by solving linear equations. The former utilizes the fastest growth of the Chebyshev polynomial among same degree polynomials; the latter employs the traditional idea of shift-invert, for which we address the important issue of automatic choice of shifts and propose a practical method for solving the shifted linear equations inside the block Davidson method. Our two filters can efficiently generate high-quality basis vectors to augment the projection subspace at each Davidson iteration step, which allows a restart scheme using an active projection subspace of small dimension. This makes our algorithms memory-economical, thus practical for large PEVD/PSVD calculations. We compare our algorithms with representative methods, including ARPACK, PROPACK, the randomized SVD method, and the limited memory SVD method. Extensive numerical tests on representative datasets demonstrate that, in general, our methods have similar or faster convergence speed in terms of CPU time, while requiring much lower memory comparing with other methods. The much lower memory requirement makes our methods more practical for large-scale PEVD/PSVD computations.
关键词	partial EVD/SVD polynomial filter rational filter kernel graph
DOI	10.1007/s11425-016-0274-0
语种	英语
WOS研究方向	Mathematics
WOS类目	Mathematics, Applied ; Mathematics
WOS记录号	WOS:000380212100013
出版者	SCIENCE PRESS
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/23275
专题	计算数学与科学工程计算研究所
通讯作者	Zhou Yunkai
作者单位	1.Southern Methodist Univ, Dept Math, Dallas, TX 75275 USA 2.Chinese Acad Sci, Acad Math & Syst Sci, Inst Computat Math & Sci Engn Comp, LSEC, Beijing 100190, Peoples R China
推荐引用方式 GB/T 7714	Zhou Yunkai,Wang Zheng,Zhou Aihui. Accelerating large partial EVD/SVD calculations by filtered block Davidson methods[J]. SCIENCE CHINA-MATHEMATICS,2016,59(8):1635-1662.
APA	Zhou Yunkai,Wang Zheng,&Zhou Aihui.(2016).Accelerating large partial EVD/SVD calculations by filtered block Davidson methods.SCIENCE CHINA-MATHEMATICS,59(8),1635-1662.
MLA	Zhou Yunkai,et al."Accelerating large partial EVD/SVD calculations by filtered block Davidson methods".SCIENCE CHINA-MATHEMATICS 59.8(2016):1635-1662.