Book Description:
The field of computational sciences has seen a considerable development in mathematics, engineering sciences, and economic equilibrium theory. Researchers in this field are faced with the problem of solving a variety of equations or variational inequalities. In computational sciences, the practice of numerical analysis for finding such solutions is essentially connected to variants of Newton's method. The efficient and iterative methods for finding the solutions of nonlinear equations or variational inclusions are presented in this book. Also discussed herein is the study of applications of these methods in engineering and biosciences problems whose formulations are nonlinear equations or variational inequalities. (Imprint: Nova)

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Table of Contents:
Preface pp. i-xi

Part 1: Efficient Iterative Processes pp.1-2

Chapter 1. Two--step methods of height efficiency index pp.3-36

Chapter 2. Numerical methods under slantly-differentiability pp.37-48

Chapter 3. H-convergence pp.49-60

Chapter 4. Chebyshev--Secant--type methods pp.61-72

Chapter 5. Convergence using recurrent functions pp.73-98

Chapter 6. ù-convergence pp.99-108

Chapter 7. Gauss--Newton method pp.109-122

Chapter 8. Convergence on K-normed spaces pp.123-136

Chapter 9. Newton's method on spaces with convergence structure pp.137-152

Part 2: Mathematical Modelling pp.153-154

Chapter 10. Newton's method and interior point techniques pp.155-158

Chapter 11. Finite element methods pp.159-164

Chapter 12. Convergence in Riemannian manifolds pp.165-170

Chapter 13. Convergence on Lie groups pp.171-180

Chapter 14. The shadowing lemma for operators with chaotic behaviour pp.181-186

Chapter 15. Conditioning of semi-definite programs pp.187-194

Chapter 16. Optimal shape design problems pp.195-204

Chapter 17. Variational inequalities pp.205-220

Chapter 18. Directional Secant-type methods pp.221-232

Chapter 19. Directional Newton-type methods pp.233-244

Chapter 20. Directional two-step methods pp.245-264

Chapter 21. ô-estimation for nonlinear regression models pp.265-276

Chapter 22. Tabaistic regression pp.277-282

Chapter 23. Hyperbolastic growth models and applications pp.283-290

Bibliography pp.291-340

Glossary of Symbols pp.341-342

Index pp.343-345