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

doi:10.1007/s11425-016-0274-0

CORC > 数学与系统科学研究院 > 中国科学院数学与系统科学研究院 > 计算数学与科学工程计算研究所

	Accelerating large partial EVD/SVD calculations by filtered block Davidson methods
	Zhou Yunkai 1; Wang Zheng 1; Zhou Aihui2
刊名	SCIENCE CHINA-MATHEMATICS
	2016-08-01
卷号	59 期号:8 页码:1635-1662
关键词	partial EVD/SVD polynomial filter rational filter kernel graph
ISSN号	1674-7283
DOI	10.1007/s11425-016-0274-0
英文摘要	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.
WOS研究方向	Mathematics
语种	英语
出版者	SCIENCE PRESS
WOS记录号	WOS:000380212100013
内容类型	期刊论文
源URL	[http://ir.amss.ac.cn/handle/2S8OKBNM/23274]
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.