Trace-Penalty Minimization for Large-scale Eigenspace Computation

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dc.contributor.authorWen, Zaiwenen_US
dc.contributor.authorYang, Chaoen_US
dc.contributor.authorLiu, Xinen_US
dc.contributor.authorZhang, Yinen_US
dc.date.accessioned2018-06-19T17:48:48Zen_US
dc.date.available2018-06-19T17:48:48Zen_US
dc.date.issued2013-02en_US
dc.date.noteFebruary 2013en_US
dc.description.abstractThe 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 an extent, their parallel scalability, limited by some inherent sequentiality, 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 heavily dominated by dense matrixmatrix 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.en_US
dc.format.extent34 ppen_US
dc.identifier.citationWen, Zaiwen, Yang, Chao, Liu, Xin, et al.. "Trace-Penalty Minimization for Large-scale Eigenspace Computation." (2013) <a href="https://hdl.handle.net/1911/102215">https://hdl.handle.net/1911/102215</a>.en_US
dc.identifier.digitalTR13-03en_US
dc.identifier.urihttps://hdl.handle.net/1911/102215en_US
dc.language.isoengen_US
dc.titleTrace-Penalty Minimization for Large-scale Eigenspace Computationen_US
dc.typeTechnical reporten_US
dc.type.dcmiTexten_US
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