Trace-Penalty Minimization for Large-Scale Eigenspace Computation

doi:10.1007/s10915-015-0061-0

	Trace-Penalty Minimization for Large-Scale Eigenspace Computation
	Wen, Zaiwen 1; Yang, Chao 2; Liu, Xin3 ; Zhang, Yin 4
	2016-03-01
发表期刊	JOURNAL OF SCIENTIFIC COMPUTING
ISSN	0885-7474
卷号	66 期号:3 页码:1175-1203
摘要	In a block algorithm for computing relatively high-dimensional eigenspaces of large sparse symmetric matrices, the Rayleigh-Ritz (RR) procedure often constitutes a major bottleneck. Although dense eigenvalue calculations for subproblems in RR steps can be parallelized to a certain level, their parallel scalability, which is limited by some inherent sequential steps, is lower than dense matrix-matrix multiplications. The primary motivation of this paper is to develop a methodology that reduces the use of the RR procedure in exchange for matrix-matrix multiplications. We propose an unconstrained trace-penalty minimization model and establish its equivalence to the eigenvalue problem. With a suitably chosen penalty parameter, this model possesses far fewer undesirable full-rank stationary points than the classic trace minimization model. More importantly, it enables us to deploy algorithms that makes heavy use of dense matrix-matrix multiplications. Although the proposed algorithm does not necessarily reduce the total number of arithmetic operations, it leverages highly optimized operations on modern high performance computers to achieve parallel scalability. Numerical results based on a preliminary implementation, parallelized using OpenMP, show that our approach is promising.
关键词	Eigenvalue computation Exact quadratic penalty approach Gradient methods
DOI	10.1007/s10915-015-0061-0
语种	英语
资助项目	Office of Advanced Scientific Computing Research of the U.S. Department of Energy[DE-AC02-05CH11232]
WOS研究方向	Mathematics
WOS类目	Mathematics, Applied
WOS记录号	WOS:000369911500013
出版者	SPRINGER/PLENUM PUBLISHERS
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/22005
专题	计算数学与科学工程计算研究所
通讯作者	Wen, Zaiwen
作者单位	1.Peking Univ, Beijing Int Ctr Math Res, Beijing, Peoples R China 2.Univ Calif Berkeley, Lawrence Berkeley Natl Lab, Computat Res Div, Berkeley, CA 94720 USA 3.Chinese Acad Sci, Acad Math & Syst Sci, State Key Lab Sci & Engn Comp, Beijing, Peoples R China 4.Rice Univ, Dept Computat & Appl Math, Houston, TX USA
推荐引用方式 GB/T 7714	Wen, Zaiwen,Yang, Chao,Liu, Xin,et al. Trace-Penalty Minimization for Large-Scale Eigenspace Computation[J]. JOURNAL OF SCIENTIFIC COMPUTING,2016,66(3):1175-1203.
APA	Wen, Zaiwen,Yang, Chao,Liu, Xin,&Zhang, Yin.(2016).Trace-Penalty Minimization for Large-Scale Eigenspace Computation.JOURNAL OF SCIENTIFIC COMPUTING,66(3),1175-1203.
MLA	Wen, Zaiwen,et al."Trace-Penalty Minimization for Large-Scale Eigenspace Computation".JOURNAL OF SCIENTIFIC COMPUTING 66.3(2016):1175-1203.