On Optimizing the Sum of Rayleigh Quotients on the Unit Sphere

Author

Aohud Abdulrahman Binbuhaer

Graduation Semester and Year

2019

Language

English

Document Type

Dissertation

Degree Name

Doctor of Philosophy in Mathematics

Department

Mathematics

First Advisor

Ren-Cang Li

Abstract

Given symmetric matrices and positive definite matrices, we are concerned with the solution of the maximization of the function that is mentioned in the dissertation. We establish necessary optimality conditions for local maximizers. Moreover, a self-consistent-field (SCF) iterative method for solving this maximization problem is introduced and analyzed. We use the Trust-Region SCF iteration to improve the convergence of the SCF method.

Keywords

Rayleigh quotient

Disciplines

Mathematics | Physical Sciences and Mathematics

License

This work is licensed under a Creative Commons Attribution-NonCommercial-Share Alike 4.0 International License.

Comments

Degree granted by The University of Texas at Arlington

Recommended Citation

Binbuhaer, Aohud Abdulrahman, "On Optimizing the Sum of Rayleigh Quotients on the Unit Sphere" (2019). Mathematics Dissertations. 183.
https://mavmatrix.uta.edu/math_dissertations/183