ABSTRACT

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.

chapter 1|24 pages

Halley’s method

ByIoannis K. Argyros, Á. Alberto Magreñán

chapter 2|21 pages

Newton’s method for k-Frechet differentiable operators

ByIoannis K. Argyros, A. Alberto Magreñanb

chapter 3|17 pages

Nonlinear Ill-posed equations

ByIoannis K. Argyros, A. Alberto Magrenan

chapter 4|25 pages

Sixth-order iterative methods

ByIoannis K. Argyros, A. Alberto Magrenan

chapter 6|11 pages

Extending the Kantorovich theory for solving equations

ByIoannis K. Argyros, A. Alberto Magreñán

chapter 7|25 pages

Robust convergence for inexact Newton method

ByIoannis K. Argyros, A. Alberto Magrenan

chapter 8|17 pages

Inexact Gauss-Newton method for least square problems

ByIoannis K. Argyros, Á. Alberto Magrenan

chapter 9|15 pages

Lavrentiev Regularization methods for Ill-posed equations

ByIoannis K. Argyros, A. Alberto Magreñán

chapter 10|17 pages

King-Werner-type methods of order 1 +√2

ByIoannis K. Argyros, Á. Alberto Magreñàn

chapter 11|11 pages

Generalized equations and Newton’s and method

ByIoannis K. Argyros, Á. Alberto Magreñán

chapter 12|12 pages

Newton’s method for generalized equations using restricted domains

ByIoannis K. Argyros, Á. Alberto Magreñán

chapter 13|25 pages

Secant-like methods

ByIoannis K. Argyros, Á. Alberto Magreñán

chapter 14|10 pages

King-Werner-like methods free of derivatives

ByIoannis K. Argyros, Á. Alberto Magreñán

chapter 15|8 pages

Muller’s method

ByIoannis K. Argyros, Á. Alberto Magrenan

chapter 16|12 pages

Generalized Newton method with applications

ByIoannis K. Argyros, Á. Alberto Magrenan

chapter 17|11 pages

Newton-secant methods with values in a cone

ByIoannis K. Argyros, Á. Alberto Magreñán

chapter 18|13 pages

Gauss-Newton method with applications to convex optimization

ByIoannis K. Argyros, Á. Alberto Magreñán

chapter 19|11 pages

Directional Newton methods and restricted domains

ByIoannis K. Argyros, Á. Alberto Magreñán

chapter 21|12 pages

Ball Convergence for eighth order method

ByIoannis K. Argyros, Á. Alberto Magrenan

chapter 22|12 pages

Expanding Kantorovich’s theorem for solving generalized equations

ByIoannis K. Argyros, Á. Alberto Magreñán