Open Access. Powered by Scholars. Published by Universities.®
Numerical Analysis and Computation Commons™
Open Access. Powered by Scholars. Published by Universities.®
- Discipline
Articles 1 - 2 of 2
Full-Text Articles in Numerical Analysis and Computation
Longitudinal Partitioning Waveform Relaxation Methods For The Analysis Of Transmission Line Circuits, Tarik Menkad
Longitudinal Partitioning Waveform Relaxation Methods For The Analysis Of Transmission Line Circuits, Tarik Menkad
Electronic Thesis and Dissertation Repository
Three research projects are presented in this manuscript. Projects one and two describe two waveform relaxation algorithms (WR) with longitudinal partitioning for the time-domain analysis of transmission line circuits. Project three presents theoretical results about the convergence of WR for chains of general circuits.
The first WR algorithm uses a assignment-partition procedure that relies on inserting external series combinations of positive and negative resistances into the circuit to control the speed of convergence of the algorithm. The convergence of the subsequent WR method is examined, and fast convergence is cast as a generic optimization problem in the frequency-domain. An automatic …
Hybrid Symbolic-Numeric Computing In Linear And Polynomial Algebra, Leili Rafiee Sevyeri
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 …