Iterative Algorithms I

Ioannis K Argyros

ISBN 10: 1634854063 / ISBN 13: 9781634854061

Edité par Nova Science Publishers Inc Sep 2016, 2016

A propos de cet article

Neuware - It is a well-known fact that iterative methods have been studied concerning problems where mathematicians cannot find a solution in a closed form. There exist methods with different behaviors when they are applied to different functions and methods with higher order of convergence, methods with great zones of convergence, methods which do not require the evaluation of any derivative, and optimal methods among others. It should come as no surprise, therefore, that researchers are developing new iterative methods frequently. Once these iterative methods appear, several researchers study them in different terms: convergence conditions, real dynamics, complex dynamics, optimal order of convergence, etc. These phenomena motivated the authors to study the most used and classical ones, for example Newton's method, Halleys method and/or its derivative-free alternatives. Related to the convergence of iterative methods, the most well-known conditions are the ones created by Kantorovich, who developed a theory which has allowed many researchers to continue and experiment with these conditions. Many authors in recent years have studied modifications of these conditions related, for example, to centered conditions, omega-conditions and even convergence in Hilbert spaces. In this monograph, the authors present their complete work done in the past decade in analysing convergence and dynamics of iterative methods. It is the natural outgrowth of their related publications in these areas. Chapters are self-contained and can be read independently. Moreover, an extensive list of references is given in each chapter in order to allow the reader to use the previous ideas. For these reasons, the authors think that several advanced courses can be taught using this book. The book's results are expected to help find applications in many areas of applied mathematics, engineering, computer science and real problems. As such, this monograph is suitable to researchers, graduate students and seminar instructors in the above subjects. The authors believe it would also make an excellent addition to all science and engineering libraries.

N° de réf. du vendeur 9781634854061

Détails bibliographiques

• Titre: Iterative Algorithms I
• Éditeur: Nova Science Publishers Inc Sep 2016
• Date de parution: 2016
• Langue: anglais
• ISBN à 10 chiffres: 1634854063
• ISBN à 13 chiffres: 9781634854061
• Reliure: Buch
• État de l'article: Neu
• Dimensions: 262 L x 183 H x 28 P (en millimètres) 262 millimètres de largeur par 183 millimètres de hauteur par 28 millimètres de profondeur
• Poids: 944 grammes

A propos de ce titre

Synopsis

It is a well-known fact that iterative methods have been studied concerning problems where mathematicians cannot find a solution in a closed form. There exist methods with different behaviors when they are applied to different functions and methods with higher order of convergence, methods with great zones of convergence, methods which do not require the evaluation of any derivative, and optimal methods among others. It should come as no surprise, therefore, that researchers are developing new iterative methods frequently. Once these iterative methods appear, several researchers study them in different terms: convergence conditions, real dynamics, complex dynamics, optimal order of convergence, etc. These phenomena motivated the authors to study the most used and classical ones, for example Newton's method, Halley s method and/or its derivative-free alternatives. Related to the convergence of iterative methods, the most well-known conditions are the ones created by Kantorovich, who developed a theory which has allowed many researchers to continue and experiment with these conditions. Many authors in recent years have studied modifications of these conditions related, for example, to centered conditions, omega-conditions and even convergence in Hilbert spaces. In this monograph, the authors present their complete work done in the past decade in analysing convergence and dynamics of iterative methods. It is the natural outgrowth of their related publications in these areas. Chapters are self-contained and can be read independently. Moreover, an extensive list of references is given in each chapter in order to allow the reader to use the previous ideas. For these reasons, the authors think that several advanced courses can be taught using this book. The book's results are expected to help find applications in many areas of applied mathematics, engineering, computer science and real problems. As such, this monograph is suitable to researchers, graduate students and seminar instructors in the above subjects. The authors believe it would also make an excellent addition to all science and engineering libraries.

À propos de l?auteur

Professor, Department of Mathematical Sciences, Cameron University, Lawton, Oklahoma, USA.