Numerical Analysis and Computation Commons^™

Hybrid Symbolic-Numeric Computing In Linear And Polynomial Algebra, Leili Rafiee Sevyeri

Electronic Thesis and Dissertation Repository

In this thesis, we introduce hybrid symbolic-numeric methods for solving problems in linear and polynomial algebra. We mainly address the approximate GCD problem for polynomials, and problems related to parametric and polynomial matrices. For symbolic methods, our main concern is their complexity and for the numerical methods we are more concerned about their stability. The thesis consists of 5 articles which are presented in the following order:

Chapter 1, deals with the fundamental notions of conditioning and backward error. Although our results are not novel, this chapter is a novel explication of conditioning and backward error that underpins the rest …