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Trace-Penalty Minimization for Large-Scale Eigenspace Computation

文献类型：期刊论文

作者Wen, Zaiwen1; Yang, Chao2; Liu, Xin3; Zhang, Yin4
刊名JOURNAL OF SCIENTIFIC COMPUTING
出版日期2016-03-01
卷号66期号:3页码:1175-1203
关键词Eigenvalue computation Exact quadratic penalty approach Gradient methods
ISSN号0885-7474
DOI10.1007/s10915-015-0061-0
英文摘要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.
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
语种英语
WOS记录号WOS:000369911500013
出版者SPRINGER/PLENUM PUBLISHERS
源URL[http://ir.amss.ac.cn/handle/2S8OKBNM/22004]  
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.

入库方式： OAI收割

来源：数学与系统科学研究院

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