An Inverse Free Projected Gradient Descent Method for the Generalized Eigenvalue Problem

dc.contributor.authorCamacho, Frankieen_US
dc.date.accessioned2018-06-19T17:51:22Zen_US
dc.date.available2018-06-19T17:51:22Zen_US
dc.date.issued2017-05en_US
dc.date.noteMay 2017en_US
dc.descriptionThis work was also published as a Rice University thesis/dissertation: http://hdl.handle.net/1911/96001en_US
dc.description.abstractThe 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.extent148 ppen_US
dc.identifier.citationCamacho, 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.digitalTR17-09en_US
dc.identifier.urihttps://hdl.handle.net/1911/102255en_US
dc.language.isoengen_US
dc.titleAn Inverse Free Projected Gradient Descent Method for the Generalized Eigenvalue Problemen_US
dc.typeTechnical reporten_US
dc.type.dcmiTexten_US
Files
Original bundle
Now showing 1 - 1 of 1
Loading...
Thumbnail Image
Name:
TR17-09.pdf
Size:
3.57 MB
Format:
Adobe Portable Document Format