From power grids to social networks to neuroscience, networks are increasingly important in science today. They are, however, inherently hard to study. On one hand, phenomena beginning in one part of a network can have complex and global effects on the rest of the network, and so behavior is frequently difficult to predict without simulations. On the other hand, modern networks are often massive, containing hundreds of millions or even billions of nodes. Due to this, network computations often require specialized algorithms that exploit network structure to perform their tasks efficiently.
In this work, we study matrix-based network computations and the relationship between network structure and linear algorithms. Out algorithms use either low rank upates or coarse grid projections to transform the problem into a smaller one that is exactly or approximately equivalent to the original. We refer to these techniques as error flattening methods.
We present three examples: a method for fast detection and identification of power grid topology errors; a nonlinear multigrid method to solve the power flow equations; and a two-part iterative method to solve graph Laplacian systems.
|School Location:||United States -- New York|
|Source:||DAI-B 78/04(E), Dissertation Abstracts International|
|Subjects:||Applied Mathematics, Electrical engineering, Computer science|
|Keywords:||Graph laplacian, Multigrid, Power grids, Topology processing|
Copyright in each Dissertation and Thesis is retained by the author. All Rights Reserved
The supplemental file or files you are about to download were provided to ProQuest by the author as part of a
dissertation or thesis. The supplemental files are provided "AS IS" without warranty. ProQuest is not responsible for the
content, format or impact on the supplemental file(s) on our system. in some cases, the file type may be unknown or
may be a .exe file. We recommend caution as you open such files.
Copyright of the original materials contained in the supplemental file is retained by the author and your access to the
supplemental files is subject to the ProQuest Terms and Conditions of use.
Depending on the size of the file(s) you are downloading, the system may take some time to download them. Please be