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oai:www.ideals.illinois.edu:2142/49413 2023-07-11 col_2142_5131 col_2142_10761 com_2142_5130 com_2142_10755 com_2142_234

Dankowicz, Harry Mallya, Pratik 2014-05-30T16:42:42Z 2014-05-30T16:42:42Z 2014-05 2014-05-30T16:42:42Z 2014-05 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. Item withdrawn by Laura Spradlin (lspradl2@illinois.edu) on 2013-12-17T22:34:16Z Item was in collections: University of Illinois Theses & Dissertations (ID: 1) No. of bitstreams: 1 Mallya_Pratik.pdf: 557340 bytes, checksum: 1dd51cd3a8f376728ef9eb4021f9afe8 (MD5) Made available in DSpace on 2014-05-30T16:42:42Z (GMT). No. of bitstreams: 2 Pratik_Mallya.pdf: 557278 bytes, checksum: 777c22eec0ec310460addbc5ba1c74c5 (MD5) license.txt: 4065 bytes, checksum: b31f3f60d1baccc9420aad3ebec631d1 (MD5) http://hdl.handle.net/2142/49413 en Copyright 2014 Pratik Mallya Numerical Continuation Atlas Algorithms Higher Dimensional Manifolds On the problem of parallelizing manifold covering algorithms text Computer Science 1434 Computer Science 0112 University of Illinois at Urbana-Champaign Thesis M.S. MS:Computer Science -UIUC 10KS0112MS