Parallel schemes for global interative zero-finding.

• Other Authors: Luk, Wai Shing.
• Format: Others
• Language: English
• Published: Chinese University of Hong Kong 1993
• Subjects: Zero (The number) > Data processing; Polynomials; Bifurcation theory; Homotopy theory
• Online Access: http://library.cuhk.edu.hk/record=b5887824; http://repository.lib.cuhk.edu.hk/en/item/cuhk-319139

by Luk Wai Shing. === Thesis (M.Phil.)--Chinese University of Hong Kong, 1993. === Includes bibliographical references (leaves 44-45). === ABSTRACT --- p.i === ACKNOWLEDGMENTS --- p.ii === Chapter CHAPTER 1. --- INTRODUCTION --- p.1 === Chapter CHAPTER 2. --- DRAWBACKS OF CLASSICAL THEORY --- p.4 === Chapter 2.1 --- Review of Sequential Iterative Methods --- p.4 === Chapter 2.2 --- Visualization Techniques --- p.8 === Chapter 2.3 --- Review of Deflation --- p.10 === Chapter CHAPTER 3. --- THE IMPROVEMENT OF THE ABERTH METHOD --- p.11 === Chapter 3.1 --- The Durand-Kerner method and the Aberth method --- p.11 === Chapter 3.2 --- The generalized Aberth method --- p.13 === Chapter 3.3 --- The modified Aberth Method for multiple-zero --- p.13 === Chapter 3.4 --- Choosing the initial approximations --- p.15 === Chapter 3.5 --- Multiplicity estimation --- p.16 === Chapter CHAPTER 4. --- THE HIGHER-ORDER ITERATIVE METHODS --- p.18 === Chapter 4.1 --- Introduction --- p.18 === Chapter 4.2 --- Convergence analysis --- p.20 === Chapter 4.3 --- Numerical Results --- p.28 === Chapter CHAPTER 5. --- PARALLEL DEFLATION --- p.32 === Chapter 5.1 --- The Algorithm --- p.32 === Chapter 5.2 --- The Problem of Zero Component --- p.34 === Chapter 5.3 --- The Problem of Round-off Error --- p.35 === Chapter CHAPTER 6. --- HOMOTOPY ALGORITHM --- p.36 === Chapter 6.1 --- Introduction --- p.36 === Chapter 6.2 --- Choosing Q(z) --- p.37 === Chapter 6.3 --- The arclength continuation method --- p.38 === Chapter 6.4 --- The bifurcation problem --- p.40 === Chapter 6.5 --- The suggested improvement --- p.41 === Chapter CHAPTER 7. --- CONCLUSION --- p.42 === REFERENCES --- p.44 === APPENDIX A. PROGRAM LISTING --- p.A-l === APPENDIX B. COLOR PLATES --- p.B-l