Block Algorithms with Augmented Rayleigh-Ritz Projections for Large-Scale Eigenpair Computation
| dc.contributor.author | Wen, Zaiwen | en_US |
| dc.contributor.author | Zhang, Yin | en_US |
| dc.date.accessioned | 2018-06-19T17:49:54Z | en_US |
| dc.date.available | 2018-06-19T17:49:54Z | en_US |
| dc.date.issued | 2015-06 | en_US |
| dc.date.note | June 2015 | en_US |
| dc.description.abstract | Most iterative algorithms for eigenpair computation consist 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. So far the predominant methodology for the SU step is based on Krylov subspaces that builds orthonormal bases piece by piece in a sequential manner. In this work, we investigate block methods in the SU step that allow a higher level of concurrency than what is reachable by Krylov subspace methods. To achieve a competitive speed, we propose an augmented Rayleigh-Ritz (ARR) procedure and analyze its rate of convergence under realistic conditions. Combining this ARR procedure with a set of polynomial accelerators, as well as utilizing a few other techniques such as continuation and deflation, we construct a block algorithm designed to reduce the number of RR steps and elevate concurrency in the SU steps. Extensive computational experiments are conducted in Matlab on a representative set of test problems to evaluate the performance of two variants of our algorithm in comparison to two well-established, high-quality eigensolvers ARPACK and FEAST. Numerical results, obtained on a many-core computer without explicit code parallelization, show that when computing a relatively large number of eigenpairs, the performance of our algorithms is competitive with, and frequently superior to, that of the two state-of-the-art eigensolvers. | en_US |
| dc.format.extent | 29 pp | en_US |
| dc.identifier.citation | Wen, Zaiwen and Zhang, Yin. "Block Algorithms with Augmented Rayleigh-Ritz Projections for Large-Scale Eigenpair Computation." (2015) <a href="https://hdl.handle.net/1911/102230">https://hdl.handle.net/1911/102230</a>. | en_US |
| dc.identifier.digital | TR15-01 | en_US |
| dc.identifier.uri | https://hdl.handle.net/1911/102230 | en_US |
| dc.language.iso | eng | en_US |
| dc.title | Block Algorithms with Augmented Rayleigh-Ritz Projections for Large-Scale Eigenpair Computation | en_US |
| dc.type | Technical report | en_US |
| dc.type.dcmi | Text | en_US |
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