Symmetric positive definite (SPD) matrices have become fundamental computational objects in many areas. It is often of interest to average a collection of symmetric positive definite matrices. This dissertation investigates different averaging techniques for symmetric positive definite matrices. We use recent developments in Riemannian optimization to develop efficient and robust algorithms to handle this computational task. We provide methods to produce efficient numerical representations of geometric objects that are required for Riemannian optimization methods on the manifold of symmetric positive definite matrices. In addition, we offer theoretical and empirical suggestions on how to choose between various methods and parameters. In the end, we evaluate the performance of different averaging techniques in applications. / A Dissertation submitted to the Department of Mathematics in partial fulfillment of the requirements for the degree of Doctor of Philosophy. / Summer Semester 2018. / July 20, 2018. / Includes bibliographical references. / Kyle A. Gallivan, Professor Co-Directing Dissertation; Pierre-Antoine Absil, Professor Co-Directing Dissertation; Gordon Erlebacher, University Representative; Giray Okten, Committee Member; Martin Bauer, Committee Member.
| Identifer | oai:union.ndltd.org:fsu.edu/oai:fsu.digital.flvc.org:fsu_647322 |
| Contributors | Yuan, Xinru (author), Gallivan, Kyle A., 1958- (professor co-directing dissertation), Absil, Pierre-Antoine (professor co-directing dissertation), Erlebacher, Gordon, 1957- (university representative), Ökten, Giray (committee member), Bauer, Martin (committee member), Florida State University (degree granting institution), College of Arts and Sciences (degree granting college), Department of Mathematics (degree granting departmentdgg) |
| Publisher | Florida State University |
| Source Sets | Florida State University |
| Language | English, English |
| Detected Language | English |
| Type | Text, text, doctoral thesis |
| Format | 1 online resource (164 pages), computer, application/pdf |
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