Date of Award
Spring 5-1-2021
Degree Type
Dissertation
Degree Name
Doctor of Philosophy (PhD)
School
Mathematics and Natural Sciences
Committee Chair
James V. Lambers
Committee Chair School
Mathematics and Natural Sciences
Committee Member 2
Jiu Ding
Committee Member 2 School
Mathematics and Natural Sciences
Committee Member 3
Haiyan Tian
Committee Member 3 School
Mathematics and Natural Sciences
Committee Member 4
John Harris
Committee Member 4 School
Mathematics and Natural Sciences
Abstract
Optimizing the approximation of bilinear forms using a one-sided perturbation, where the computation of the approximate solution is generated faster while using less storage or reusing information is possible. Standard methods for approximation like Lanczos and others exist; however, separating the work a little bit and having the bilinear form relate to the quadratic form can yield a more efficient algorithm. When we have an application where the needs are different, it is helpful to understand how the processes like symmetric Lanczos and unsymmetric Lanczos relate to one another so that we can find a way to break things down to accommodate specific cases. The objective of this research is to build an efficient algorithm to approximate bilinear forms with matrix functions utilizing the quadrature rule for approximating quadratic forms without applying the standard methods of approximation.
Copyright
Altheimer, 2021
Recommended Citation
Altheimer, Keelia, "On the Treatment of Bilinear Forms Involving Matrix Functions as Perturbations of Quadratic Forms" (2021). Dissertations. 1887.
https://aquila.usm.edu/dissertations/1887