Iterative methods for roots of polynomials
We describe iterative methods for polynomial zero finding and, specifically, the Laguerre method and how it is used in the NAG subroutine C02AFF. We also investigate a bug that has been in this subroutine for ten years. In chapter two, we give a brief survey of some zero finding methods. These inclu...
| Main Author: | |
|---|---|
| Format: | Thesis |
| Published: |
University of Oxford;Mathematical Institute
2001
|
| _version_ | 1826312169814228992 |
|---|---|
| author | Mekwi, W |
| author_facet | Mekwi, W |
| author_sort | Mekwi, W |
| collection | OXFORD |
| description | We describe iterative methods for polynomial zero finding and, specifically, the Laguerre method and how it is used in the NAG subroutine C02AFF. We also investigate a bug that has been in this subroutine for ten years. In chapter two, we give a brief survey of some zero finding methods. These include Bairstow's method, Bernoulli's method, Graeffe's root-squaring method, Müller's method, the Newton-Raphson method and the Jenkins-Traub and Laguerre methods. In chapter three, we look at the Laguerre method as used in C02AFF in further detail, describe the behaviour of the bug and how the problem has been solved. We also describe general tests for zero finding algorithms and results of comparisons between NAG's C02AFF and other zero finding programs. Chapter 4 involves comparisons of C02AFF with other methods and a note on error bounds. Finally, we make our proposals and conclusions in chapter 5. |
| first_indexed | 2024-03-07T08:25:00Z |
| format | Thesis |
| id | oxford-uuid:a1cb2db7-b587-4a0f-a442-dc3e06797726 |
| institution | University of Oxford |
| last_indexed | 2024-03-07T08:25:00Z |
| publishDate | 2001 |
| publisher | University of Oxford;Mathematical Institute |
| record_format | dspace |
| spelling | oxford-uuid:a1cb2db7-b587-4a0f-a442-dc3e067977262024-02-12T11:35:15ZIterative methods for roots of polynomialsThesishttp://purl.org/coar/resource_type/c_db06uuid:a1cb2db7-b587-4a0f-a442-dc3e06797726Mathematical Institute - ePrintsUniversity of Oxford;Mathematical Institute2001Mekwi, WWe describe iterative methods for polynomial zero finding and, specifically, the Laguerre method and how it is used in the NAG subroutine C02AFF. We also investigate a bug that has been in this subroutine for ten years. In chapter two, we give a brief survey of some zero finding methods. These include Bairstow's method, Bernoulli's method, Graeffe's root-squaring method, Müller's method, the Newton-Raphson method and the Jenkins-Traub and Laguerre methods. In chapter three, we look at the Laguerre method as used in C02AFF in further detail, describe the behaviour of the bug and how the problem has been solved. We also describe general tests for zero finding algorithms and results of comparisons between NAG's C02AFF and other zero finding programs. Chapter 4 involves comparisons of C02AFF with other methods and a note on error bounds. Finally, we make our proposals and conclusions in chapter 5. |
| spellingShingle | Mekwi, W Iterative methods for roots of polynomials |
| title | Iterative methods for roots of polynomials |
| title_full | Iterative methods for roots of polynomials |
| title_fullStr | Iterative methods for roots of polynomials |
| title_full_unstemmed | Iterative methods for roots of polynomials |
| title_short | Iterative methods for roots of polynomials |
| title_sort | iterative methods for roots of polynomials |
| work_keys_str_mv | AT mekwiw iterativemethodsforrootsofpolynomials |