Computational Methods in Nonlinear Analysis

Efficient Algorithms, Fixed Point Theory and Applications

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. We note that in computational sciences, the practice of numerical analysis for finding such solutions is essentially connected to variants of Newton's method. The efficient computational methods for finding the solutions of fixed point problems, nonlinear equations and variational inclusions are the first goal of the present book. The second goal is the applications of these methods in nonlinear problems and the connection with fixed point theory.

This book is intended for researchers in computational sciences, and as a reference book for an advanced computational methods in nonlinear analysis. We collect the recent results on the convergence analysis of numerical algorithms in both finite-dimensional and infinite-dimensional spaces, and present several applications and connections with fixed point theory. The book contains abundant and updated bibliography, and provides comparison between various investigations made in recent years in the field of computational nonlinear analysis.

Contents:

• Newton's Methods
• Special Conditions for Newton's Method
• Newton's Method on Special Spaces
• Secant Method
• Gauss–Newton Method
• Halley's Method
• Chebyshev's Method
• Broyden's Method
• Newton-like Methods
• Newton–Tikhonov Method for Ill-posed Problems

Readership: Graduate students and researchers in computational mathematics and nonlinear analysis.
Key Features:

• The book contains recent results in the field of computational sciences
• The book updates the results of the 3 competing books: (1) Convergence and Applications of Newton-type iterations, springer–Verlag Publ., 2008 (author: Ioannis K Argyros) (2) Functional Analysis, Pergamon Press, Oxford, 1982 (authors: L V Kantorovich, G P Akilov) (3) Iterative Solution of Nonlinear Equations in Several Variables, Academic Press, New York, 1970 (authors: L M Ortega, W C Rheinboldt)
• The book presents several applications and examples in engineering, mathematical physics, optimization and many other areas