Purdue University Purdue e-Pubs Open Access Dissertations Theses and Dissertations January 2016 Graph diffusions and matrix functions: fast algorithms and localization results Kyle Kloster Purdue University Follow this and additional works at: https://docs.lib.purdue.edu/open_access_dissertations Recommended Citation Kloster, Kyle, "Graph diffusions and matrix functions: fast algorithms and localization results" (2016). Open Access Dissertations. 1404. https://docs.lib.purdue.edu/open_access_dissertations/1404 This document has been made available through Purdue e-Pubs, a service of the Purdue University Libraries. Please contact
[email protected] for additional information. Graduate School Form 30 Updated 12/26/2015 PURDUE UNIVERSITY GRADUATE SCHOOL Thesis/Dissertation Acceptance This is to certify that the thesis/dissertation prepared By Kyle Kloster Entitled GRAPH DIFFUSIONS AND MATRIX FUNCTIONS: FAST ALGORITHMS AND LOCALIZATION RESULTS For the degree of Doctor of Philosophy Is approved by the final examining committee: David F. Gleich Co-chair Jianlin Xia Co-chair Greg Buzzard Jie Shen To the best of my knowledge and as understood by the student in the Thesis/Dissertation Agreement, Publication Delay, and Certification Disclaimer (Graduate School Form 32), this thesis/dissertation adheres to the provisions of Purdue University’s “Policy of Integrity in Research” and the use of copyright material. David F. Gleich Approved by Major Professor(s): Greg Buzzard 4/25/2016 Approved by: Head of the Departmental Graduate Program Date GRAPH DIFFUSIONS AND MATRIX FUNCTIONS: FAST ALGORITHMS AND LOCALIZATION RESULTS A Dissertation Submitted to the Faculty of Purdue University by Kyle Kloster In Partial Fulfillment of the Requirements for the Degree of Doctor of Philosophy May 2016 Purdue University West Lafayette, Indiana ii For my big brother, who first taught me what a function is, who first made me think math looked cool, and who has always supported me.