On the problem of parallelizing manifold covering algorithms
Mallya, Pratik
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https://hdl.handle.net/2142/49413
Description
Title
On the problem of parallelizing manifold covering algorithms
Author(s)
Mallya, Pratik
Issue Date
2014-05-30T16:42:42Z
Director of Research (if dissertation) or Advisor (if thesis)
Dankowicz, Harry
Department of Study
Computer Science
Discipline
Computer Science
Degree Granting Institution
University of Illinois at Urbana-Champaign
Degree Name
M.S.
Degree Level
Thesis
Keyword(s)
Numerical Continuation
Atlas Algorithms
Higher Dimensional Manifolds
Abstract
Continuation methods are numerical algorithms used to determine the solution space of systems of nonlinear equations with
associated sets of parameters. Such methods have been very successful in computing solution manifolds of dimension one.
For higher dimensional manifolds, different techniques have been tried, with one method, Henderson's Algorithm, offering the most promise.
However, the enormous size of the systems encountered in practice, along with the high dimensionality of the solution manifold, may make the
method too slow for practical use.
This thesis evaluates an approach for the parallel computation of manifolds. We experiment with a few variations
before deciding on an approach that proves most promising. We use the COCO toolbox, written in MATLAB, for all our
experiments. In particular, we make use of MATLAB's Parallel Computing Toolbox, which provides the infrastructure
for limited parallel processing. In the course of our work, we discuss various issues faced
when computing manifolds in parallel, such as the efficient merging of manifolds and accurate estimates of performance
improvement over corresponding serial methods. In the concluding chapters, we show some results that were obtained
using our implementation and discuss improvements that might make the algorithm even more efficient.
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