Accelerating Convergence by Augmented Rayleigh-Ritz Projections For Large-Scale Eigenpair Computation

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dc.contributor.authorWen, Zaiwen
dc.contributor.authorZhang, Yin
dc.date.accessioned2018-06-19T17:50:45Z
dc.date.available2018-06-19T17:50:45Z
dc.date.issued2016-01
dc.date.noteJanuary 2016
dc.description.abstractIterative algorithms for large-scale eigenpair computation are mostly based subspace projections consisting of two main steps: a subspace update (SU) step that generates bases for approximate eigenspaces, followed by a Rayleigh-Ritz (RR) projection step that extracts approximate eigenpairs. A predominant methodology for the SU step makes use of Krylov subspaces that builds orthonormal bases piece by piece in a sequential manner. On the other hand, block methods such as the classic (simultaneous) subspace iteration, allow higher levels of concurrency than what is reachable by Krylov subspace methods, but may suffer from slow convergence. In this work, we analyze the rate of convergence for a simple block algorithmic framework that combines an augmented Rayleigh-Ritz (ARR) procedure with the subspace iteration. Our main results are Theorem 4.5 and its corollaries which show that the ARR procedure can provide significant accelerations to convergence speed. Our analysis will offer useful guidelines for designing and implementing practical algorithms from this framework.
dc.format.extent22 pp
dc.identifier.citationWen, Zaiwen and Zhang, Yin. "Accelerating Convergence by Augmented Rayleigh-Ritz Projections For Large-Scale Eigenpair Computation." (2016) <a href="https://hdl.handle.net/1911/102241">https://hdl.handle.net/1911/102241</a>.
dc.identifier.digitalTR16-01
dc.identifier.urihttps://hdl.handle.net/1911/102241
dc.language.isoeng
dc.titleAccelerating Convergence by Augmented Rayleigh-Ritz Projections For Large-Scale Eigenpair Computation
dc.typeTechnical report
dc.type.dcmiText
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