Iterative processes are the tools used to generate sequences approximating solutions of equations describing real life problems. Intended for researchers in computational sciences and as a reference book for advanced computational method in nonlinear analysis, this book is a collection of the recent results on the convergence analysis of numerical algorithms in both finite-dimensional and infinite-dimensional spaces and presents several applications and connections with fixed point theory. It contains an abundant and updated bibliography and provides comparisons between various investigations made in recent years in the field of computational nonlinear analysis.
The book also provides recent advancements in the study of iterative procedures and can be used as a source to obtain the proper method to use in order to solve a problem. The book assumes a basic background in Mathematical Statistics, Linear Algebra and Numerical Analysis and may be used as a self-study reference or as a supplementary text for an advanced course in Biosciences or Applied Sciences. Moreover, the newest techniques used to study the dynamics of iterative methods are described and used in the book and they are compared with the classical ones.
Halley’s method. Newton’s method for k-Fréchet differentiable operators. Nonlinear Ill-posed quations. Sixth-order iterative methods. Local convergence and basins of attraction of a two-step Newton like method for equations with solutions of multiplicity greater than one. Extending the Kantorovich theory for solving equations. Robust convergence for inexact Newton method. Inexact Gauss-Newton-like method for least square problems. Lavrentiev Regularization Methods for Ill-posed Equations. King-Werner-type methods of order 1+sqrt(2). Generalized equations and Newton’s method. Newton’s method for generalized equations using restricted domains. Secant-like methods. King-Werner-like methods free of derivatives. Müller’s method. Generalized Newton Method with applications. Newton-secant methods with values in a cone. Gauss-Newton method with applications to convex optimization. Directional Newton methods and restricted domains. Gauss-Newton method for convex optimization. Ball Convergence for eighth order method. Expanding Kantorovich’s theorem for solving generalized equations.