A Multigrid Solver for Graph Laplacian Linear Systems on Power-Law Graphs
| dc.contributor.advisor | Knepley, Matthew G | en_US |
| dc.creator | Buras, Eric | en_US |
| dc.date.accessioned | 2017-08-07T18:38:59Z | en_US |
| dc.date.available | 2017-08-07T18:38:59Z | en_US |
| dc.date.created | 2016-05 | en_US |
| dc.date.issued | 2016-05-17 | en_US |
| dc.date.submitted | May 2016 | en_US |
| dc.date.updated | 2017-08-07T18:38:59Z | en_US |
| dc.description.abstract | The Laplacian matrix, L, of a graph, G, contains degree and edge information of a given network. Solving a Laplacian linear system Lx = b provides information about flow through the network, and in specific cases, how that information orders the nodes in the network. I propose a novel way to solve this linear system by first partitioning G into its maximum locally-connected subgraph and a small subgraph of the remaining so-called "teleportation" edges. I then apply optimal multigrid solves to the locally-connected subgraph, and linear algebra and a solve on the teleportation subgraph to solve the original linear system. I show results for this method on real-world graphs from the biological systems of the C. Elegans worm, Facebook friend networks, and the power grid of the Western United States. | en_US |
| dc.format.mimetype | application/pdf | en_US |
| dc.identifier.citation | Buras, Eric. "A Multigrid Solver for Graph Laplacian Linear Systems on Power-Law Graphs." (2016) Master’s Thesis, Rice University. <a href="https://hdl.handle.net/1911/96624">https://hdl.handle.net/1911/96624</a>. | en_US |
| dc.identifier.uri | https://hdl.handle.net/1911/96624 | en_US |
| dc.language.iso | eng | en_US |
| dc.rights | Copyright is held by the author, unless otherwise indicated. Permission to reuse, publish, or reproduce the work beyond the bounds of fair use or other exemptions to copyright law must be obtained from the copyright holder. | en_US |
| dc.subject | Laplacian | en_US |
| dc.subject | Multigrid | en_US |
| dc.title | A Multigrid Solver for Graph Laplacian Linear Systems on Power-Law Graphs | en_US |
| dc.type | Thesis | en_US |
| dc.type.material | Text | en_US |
| thesis.degree.department | Computational and Applied Mathematics | en_US |
| thesis.degree.discipline | Engineering | en_US |
| thesis.degree.grantor | Rice University | en_US |
| thesis.degree.level | Masters | en_US |
| thesis.degree.name | Master of Arts | en_US |
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