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