This thesis presents and evaluates a generic algorithm for incrementally computing the dominant singular subspaces of a matrix. The relationship between the generality of the results and the necessary computation is explored, and it is shown that more efficient computation can be obtained by relaxing the algebraic constraints on the factoriation. The performance of this method, both numerical and computational, is discussed in terms of the algorithmic parameters, such as block size and acceptance threshhold. Bounds on the error are presented along with a posteriori approximations of these bounds. Finally, a group of methods are proposed which iteratively improve the accuracy of computed results and the quality of the bounds. / A Dissertation submitted to the School of Computational Science in partial
fulfillment of the requirements for the degree of Doctor of Philosophy. / Degree Awarded: Summer Semester, 2008. / Date of Defense: May 22, 2008. / Riemannian Manifolds, Iterative Methods, Convergence Theory, Numerical Optimization, Eigenvalue Problems, Trust-Region Methods, Riemannian Optimization, Optimization on Manifolds / Includes bibliographical references. / Kyle Gallivan, Professor Co-Directing Dissertation; Pierre-Antoine Absil, Professor Co-Directing Dissertation; Anjaneyulu Krothapalli, Outside Committee Member; Gordon Erlebacher, Committee Member; Anuj Srivastava, Committee Member; Yousuff Hussaini, Committee Member.
| Identifer | oai:union.ndltd.org:fsu.edu/oai:fsu.digital.flvc.org:fsu_169152 |
| Contributors | Baker, Christopher Grover (authoraut), Gallivan, Kyle (professor co-directing dissertation), Absil, Pierre-Antoine (professor co-directing dissertation), Krothapalli, Anjaneyulu (outside committee member), Erlebacher, Gordon (committee member), Srivastava, Anuj (committee member), Hussaini, Yousuff (committee member), Department of Scientific Computing (degree granting department), Florida State University (degree granting institution) |
| Publisher | Florida State University |
| Source Sets | Florida State University |
| Language | English, English |
| Detected Language | English |
| Type | Text, text |
| Format | 1 online resource, computer, application/pdf |
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