An Inverse Free Projected Gradient Descent Method for the Generalized Eigenvalue Problem
dc.contributor.author | Camacho, Frankie | en_US |
dc.date.accessioned | 2018-06-19T17:51:22Z | en_US |
dc.date.available | 2018-06-19T17:51:22Z | en_US |
dc.date.issued | 2017-05 | en_US |
dc.date.note | May 2017 | en_US |
dc.description | This work was also published as a Rice University thesis/dissertation: http://hdl.handle.net/1911/96001 | en_US |
dc.description.abstract | The generalized eigenvalue problem is a fundamental numerical linear algebra problem whose applications are wide ranging. For truly large-scale problems, matrices themselves are often not directly accessible, but their actions as linear operators can be probed through matrix-vector multiplications. To solve such problems, matrix-free algorithms are the only viable option. In addition, algorithms that do multiple matrix-vector multiplications simultaneously (instead of sequentially), or so-called block algorithms, generally have greater parallel scalability that can prove advantageous on highly parallel, modern computer architectures. In this work, we propose and study a new inverse-free, block algorithmic framework for generalized eigenvalue problems that is based on an extension of a recent framework called eigpen|an unconstrained optimization formulation utilizing the Courant Penalty function. We construct a method that borrows several key ideas, including projected gradient descent, back-tracking line search, and Rayleigh-Ritz (RR) projection. We establish a convergence theory for this framework. We conduct numerical experiments to assess the performance of the proposed method in comparison to two well-known existing matrix-free algorithms, as well as to the popular solver arpack as a benchmark (even though it is not matrix-free). Our numerical results suggest that the new method is highly promising and worthy of further study and development. | en_US |
dc.format.extent | 148 pp | en_US |
dc.identifier.citation | Camacho, Frankie. "An Inverse Free Projected Gradient Descent Method for the Generalized Eigenvalue Problem." (2017) <a href="https://hdl.handle.net/1911/102255">https://hdl.handle.net/1911/102255</a>. | en_US |
dc.identifier.digital | TR17-09 | en_US |
dc.identifier.uri | https://hdl.handle.net/1911/102255 | en_US |
dc.language.iso | eng | en_US |
dc.title | An Inverse Free Projected Gradient Descent Method for the Generalized Eigenvalue Problem | en_US |
dc.type | Technical report | en_US |
dc.type.dcmi | Text | en_US |
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