Eran Treister, Ph.D. Thesis Seminar
Wednesday, 11.6.2014, 11:00
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.