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Accession Number ADA585471
Title Trace-Penalty Minimization for Large-scale Eigenspace Computation.
Publication Date Mar 2013
Media Count 31p
Personal Author C. Yang X. Liu Y. Zhang Z. Wen
Abstract The Rayleigh-Ritz (RR) procedure, including orthogonalization, constitutes a major bottleneck in computing relatively high-dimensional eigenspaces of large sparse matrices. Although operations involved 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 penalty model and establish its equivalence to the eigenvalue problem. This model enables us to deploy gradient-type 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.
Keywords Algorithms
Computations
Eigenvalue computation
Eigenvalues
Exact quadratic penalty approach
Gradient methods
High performance computing
Optimization


 
Source Agency Non Paid ADAS
NTIS Subject Category 72B - Algebra, Analysis, Geometry, & Mathematical Logic
Corporate Author Rice Univ., Houston, TX. Dept. of Computational and Applied Mathematics.
Document Type Technical report
Title Note N/A
NTIS Issue Number 1403
Contract Number N00014-08-1-1101

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