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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 analyzing 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.

The study of iterative methods began several years ago in order to find the solutions of problems where mathematicians cannot find a solution in closed form. In this way, different studies related to different methods with different behaviors have been presented over the last decades. Convergence conditions have become one of the most studied topics in recent mathematical research. One of the most well-known conditions are the Kantorovich conditions, which has allowed many researchers to experiment with all kinds of conditions. In recent years, several authors have studied different modifications of the mentioned conditions considering inter alia, Hölder conditions, alpha-conditions or even convergence in other spaces. In this monograph, the authors present the complete work within the past decade on convergence and dynamics of iterative methods. It acts as an extension of their related publications in these areas. The 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 refer to previous ideas. For these reasons, several advanced courses can be taught using this book. This book intends to find applications in many areas of applied mathematics, engineering, computer science and real problems. As such, this monograph is suitable for researchers, graduate students and seminars in the above subjects, and it would be an excellent addition to all science and engineering libraries.

Algorithms were always an important part of many branches in the sciences. In many manuals and handbooks, algorithms of problems of computational mathematics are focused on the manual performance or by means of a calculator. In this book, descriptions of algorithms, their solutions and main characteristics are discussed. The present work is the outcome of many years of the authors'work on solving different problems and tasks from domains of instruction making, metrology, system analysis, ecology, data analysis from ecology, agriculture, medicine and creation of corresponding universal computer packages and systems.

Many advances have recently been made in metaheuristic methods, from theory to applications. The community of researchers claiming the relevance of their work to the field of metaheuristics is growing faster and faster, despite the fact that the term itself has not been precisely defined. This book discusses theoretical developments in metaheuristics, adaptation of discrete metaheuristics to continuous optimization, performance comparisons of metaheuristics, cooperative methods combining different approaches, parallel and distributed metaheuristics for multiobjective optimization, software implementations, and real-world applications.

This book presents and discusses research in the study of computer science. Topics discussed include biological pathways; supervised learning approaches; pathway modeling; shortest path algorithms; clustering algorithms; inductive logic programming and computationally efficient approximation schemes for functional optimization.

We are living in a world where complexity of systems created and studied by people grows beyond all imaginable limits. Computers, their software and their networks are among the most complicated systems of our time. Science is the only efficient tool for dealing with this overwhelming complexity. One of the methodologies developed in science is the axiomatic approach. It proved to be very powerful in mathematics. In this book, the authors developed further an axiomatic approach in computer science initiated by Floyd, Manna, Blum and other researchers. In the traditional constructive setting, different classes of algorithms (programs, processes or automata) are studied separately, with some indication of relations between these classes. In such a way, the constructive approach gave birth to the theory of Turing machines, theory of partial recursive functions, theory of finite automata, and other theories of constructive models of algorithms. The axiomatic context allows one to research collections of classes of algorithms, automata, and processes. These classes are united in a collection by common properties in a form of axioms. As a result, axiomatic approach goes higher in the hierarchy of computer and network models, reducing in such a way complexity of their study.

Cluster analysis has been used in a variety of fields. An algorithm is applied to the data with the purpose of dividing the elements in groups in such a way that objects in the same group are as similar as possible to each other and are as dissimilar as possible to the objects of different groups. Based on the observed values of some variables, the elements are compared using some similarity or dissimilarity measure. This new book explores the fields of clustering algorithms and mathematical modeling with research gathered from around the globe.

This book introduces a discrete optimization technique in four applications: classic Traveler Salesperson Problem (TSP), Multilocus Genetic Mapping, Multilocus Consensus Genetic Mapping, and Physical Mapping. Each of the four sections contains the problem formulation, description of the algorithm, and experimental results. The foregoing problems are solved on the basis of Guided Evolution Strategy (GES) algorithm. The algorithm was implemented in MultiPoint package (http://multiqtl.com). The developed analytical tools were applied in many genome mapping projects.

This book is an overview of the most relevant collision resolution algorithms used in contention-based multiple access protocols to handle collisions among users contending for channel access. The two main categories of collision resolution algorithms are the so called backoff and the splitting algorithms. The described backoff algorithms are further classified into p-persistent, binary exponential, X-Increase Y-Decrease and dynamic optimum backoff window algorithms. On the other hand, the splitting algorithms are basically characterized as gated-access, window-access and free-access. The dynamic tree algorithm and some limited sensing algorithms are also discussed. Other proposals that cannot be classified in the previous categories are also presented. Finally, examples of MAC protocols for wireless communications that make use of some of the aforementioned collision resolution algorithms are included.