Mathematical Modeling for the Solution of Equations and Systems of Equations with Applications. Volume II

Ioannis K. Argyros
Cameron University, Department of Mathematical Sciences, Lawton, OK, USA

Santhosh George
Department of Mathematical and Computational Sciences, NIT Karnakata, India

Narayan Thapa
Cameron University, Department of Mathematical Sciences, Lawton, OK, USA

Series: Mathematics Research Developments
BISAC: MAT017000




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This book is dedicated to the approximation of solutions of nonlinear equations using iterative methods. The study about convergence matter of iterative methods is usually based on two categories: semi-local and local convergence analysis. The semi-local convergence category is, based on the information around an initial point, to provide criteria ensuring the convergence of the method; while the local one is, based on the information around a solution, to find estimates of the radii of the convergence balls. The book is divided into two volumes. The chapters in each volume are self-contained so they can be read independently. Each chapter contains semi-local and local convergence results for single, multi-step and multi-point old and new contemporary iterative methods involving Banach, Hilbert or Euclidean valued operators. These methods are used to generate a sequence defined on the aforementioned spaces that converges with a solution of a nonlinear equation, an inverse problem or an ill-posed problem. It is worth mentioning that most problems in computational and related disciplines can be brought in the form of an equation using mathematical modelling. The solutions of equations can be found in analytical form only in special cases. Hence, it is very important to study the convergence of iterative methods.

The book is a valuable tool for researchers, practitioners, graduate students, and can also be used as a textbook for seminars in all computational and related disciplines.


Chapter 1. Unifying Semilocal and Local Convergence of Newton's Method (pp. 1-14)

Chapter 2. Higher Order Methods for Nonlinear System of Equations (pp. 15-36)

Chapter 3. Semilocal Convergence of Newton's Method (pp. 37-46)

Chapter 4. Newton-Kantorovich-Like Theorems under W Conditions (pp. 47-62)

Chapter 5. Unified Local Convergence for Newton-Kantorovich Method under W Condition (pp. 63-74)

Chapter 6. Mesh Independence for Solving Nonlinear Equations (pp. 75-88)

Chapter 7. Expanding the Applicability of Four Iterative Methods (pp. 89-102)

Chapter 8. Improved Complexity of a Homotopic Method for Locating an Approximate Zero (pp. 103-110)

Chapter 9. Convergence Analysis of Frozen Secant-Type Methods (pp. 111-128)

Chapter 10. Unified Convergence Analysis of Frozen Newton-Like Methods (pp. 129-144)

Chapter 11. Solvability of Equations Using Secant-Type Methods (pp. 145-156)

Chapter 12. Newton-Tikhonov Method for Ill-Posed Equations (pp. 157-176)

Chapter 13. Simplified Newton-Tikhonov Regularization Method (pp. 177-188)

Chapter 14. Two Step Newton Lavrentiev Method for Ill-Posed Problems (pp. 189-206)

Chapter 15. Two Step Newton-Tikhonov Methods for Ill-Posed Problems (pp. 207-228)

Chapter 16. Regularization Methods for Ill-Posed Problems (pp. 229-244)

Chapter 17. Expanding the Applicability of Lavrentiev Regularization Method (pp. 245-260)

Chapter 18. Iterated Lavrentiev Regularization (pp. 261-276)

Chapter 19. On The Semilocal Convergence of a Two-Step Newton-Like Projection Method for Ill-Posed Equations (pp. 277-296)

Chapter 20. Local Convergence of Lavrentiev Regularization for Ill-Posed Equations (pp. 297-308)

Chapter 21. Modified Gauss-Newton Method for Nonlinear Ill-Posed Problems (pp. 309-320)

Chapter 22. Two Step Newton-Type Projection Method for Ill-Posed Problems (pp. 321-344)

Chapter 23. Discretized Newtontikhonov Method for Ill-Posed Hammerstein Type Equations (pp. 345-366)

Authors Contact Information (pp. 367-368)

Index (pp. 369)

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