دانلود کتاب الگوریتم های تکراری I

It is a well-known fact that iterative methods have been studied since problems where we cannot find a solution in a closed form. There exist methods with different behaviors when they are applied to different functions, methods with higher order of convergence, methods with great zones of convergence, methods which do not require the evaluation of any derivative, etc. and researchers are developing new iterative methods frequently. Once these iterative methods appeared, several researchers have studied them in different terms: convergence conditions, real dynamics, complex dynamics, optimal order of convergence, etc. This phenomena motivated the authors to study the most used and classical ones as for example Newton’s method or its derivative-free alternative the Secant method. Related to the convergence of iterativemethods, themost well known conditions are the Kantorovich ones, who developed a theory which has allow many researchers to continue and experiment with these conditions. Many authors in the recent years have studied modifications of theses conditions related, for example, to centered conditions, w-conditions or even convergence in Hilbert spaces. In this monograph, we present the complete recent work of the past decade of the authors on 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 reader to use the previous ideas. For these reasons, we think that several advanced courses can be taught using this book.