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Aggregation-based Adaptive Algebraic Multigrid for Sparse Linear Systems
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Eran Treister, Ph.D. Thesis Seminar
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Wednesday, 11.6.2014, 11:00
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Taub 601
Algebraic Multigrid (AMG) methods have long been recognized for their efficiency as solvers of sparse linear systems of equations, mainly such that arise from discretizations of Partial Differential Equations (PDE). During the past 10 years, a great effort was invested in extending the applicability of AMG methods to other types of problems, mainly by developing adaptive versions of these methods that require fewer assumptions on the underlying systems. Our work is a part of this effort, and is comprised of three different projects. Our first project focuses on adaptive aggregation-based multigrid approaches for the solution of the Markov-chain problem, which has drawn significant recent attention, largely due to its relevance in web search applications (e.g., Google's PageRank). In our second project, we introduced a multilevel approach to l_1 penalized least squares minimization, which is widely used in the areas of sparse approximation of images/signals and compressed sensing. In our last project, we developed a sparsification mechanism for AMG approaches. This sparsification mechanism is very advantageous in parallel computations, where it reduces expensive communication overhead which is usually imposed by "traditional" AMG methods.
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