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The book is designed for researchers, students and practitioners interested in using fast and efficient iterative methods to approximate solutions of nonlinear equations. The following four major problems are addressed. Problem 1: Show that the iterates are well defined. Problem 2: concerns the convergence of the sequences generated by a process and the question of whether the limit points are, in fact solutions of the equation. Problem 3: concerns the economy of the entire operations. Problem 4: concerns with how to best choose a method, algorithm or software program to solve a specific type

Funktionalanalysis. --- Iteration. --- Iterative methods (Mathematics). --- Lehrbuch. --- Numerische Mathematik. --- Iterative methods (Mathematics) --- Engineering & Applied Sciences --- Applied Mathematics --- Numerical analysis. --- Mathematical analysis --- Iteration (Mathematics) --- Numerical analysis

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Iterative methods (Mathematics) --- Algorithms. --- Numerical analysis. --- Mathematical analysis --- Algorism --- Algebra --- Arithmetic --- Iteration (Mathematics) --- Numerical analysis --- Foundations

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Iterative methods (Mathematics) --- Numerical analysis. --- Mathematical analysis --- Iteration (Mathematics) --- Numerical analysis

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This comprehensive book delves into the intricacies of Newton-type methods for nonlinear equations, offering insights into their convergence, accelerations, and extensions. Divided into three parts, the book explores higher-order iterations for nonlinear equations and their systems, and their applications in linear algebra and some nonlinear problems of theoretical physics. Emphasizing the pivotal role of iteration parameters in shaping convergence and expanding the domain, the authors draw from their extensive collaborative research to systematically compile and elucidate these findings. Catering to readers, graduate students, and researchers in applied mathematics, numerical analysis, and related disciplines, this book serves as a valuable resource, synthesizing decades of research to advance understanding and practical application in the field.

Engineering mathematics. --- Engineering Mathematics. --- Calculus of variations. --- Iterative methods (Mathematics) --- Mathematical optimization.

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This book, written by two experts in the field, deals with classes of iterative methods for the approximate solution of fixed points equations for operators satisfying a special contractivity condition, the Fejér property. The book is elementary, self-contained and uses methods from functional analysis, with a special focus on the construction of iterative schemes. Applications to parallelization, randomization and linear programming are also considered.

Iterative methods (Mathematics) --- Numerical analysis. --- Mathematical analysis --- Iteration (Mathematics) --- Numerical analysis --- Ill-posed Problems. --- Iteration Method. --- Noisy Data. --- Nonlinear Equations. --- Optimization.