Date of Award

Spring 3-19-2021

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.

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