Michael K. Ng - Böcker

Toeplitz and Toeplitz-related systems arise in a variety of applications in mathematics and engineering, especially in signal and image processing. This book deals primarily with iterative methods for solving Toeplitz and Toeplitz-related linear systems, discussing both the algorithms and their convergence theories. A basic knowledge of real analysis, elementary numerical analysis and linear algebra is assumed.The first part of the book (chapters one and two) gives a brief review of some terms and results in linear algebra and the conjugate gradient method, which are important topics for handling the mathematics later on in the book. The second part of the book (chapters three to seven) presents the theory of using iterative methods for solving Toeplitz and Toeplitz-related systems. The third part of the book (chapters eight to twelve) presents recent results from applying the use of iterative methods in different fields of applications, such as partial differential equations, signal and image processing, integral equations and queuing networks. These chapters provide research and application-oriented readers with a thorough understanding of using iterative methods, enabling them not only to apply these methods to the problems discussed but also to derive and analyse new methods for other types of problems and applications.

Proceedings of the International Symposium on High Performance Computational Science and Engineering 2004 (IFIP World Computer Congress) is an essential reference for both academic and professional researchers in the field of computational science and engineering.Computational Science and Engineering is increasingly becoming an emerging and promising discipline in shaping future research and development activities in academia and industry ranging from engineering, science, finance, economics, arts and humanitarian fields.  New challenges are in modeling of complex systems, sophisticated algorithms, advanced scientific and engineering computing, and associated (multi-disciplinary) problem solving environments.  The papers presented in this volume are specially selected to address the most up-to-date ideas, results, work-in-progress and research experience in the area of high performance computational techniques for science and engineering applications.This state-of-the-are volume presents the proceedings of the International Symposium on High Performance Computational Science and Engineering, held  in conjunction with the IFIP World Computer Congress, August 2004, in Toulouse, France.The collection will be important not only for computational science and engineering experts and researchers but for all teachers and administrators interested in high performance computational techniques.

Proceedings of the International Symposium on High Performance Computational Science and Engineering 2004 (IFIP World Computer Congress) is an essential reference for both academic and professional researchers in the field of computational science and engineering.Computational Science and Engineering is increasingly becoming an emerging and promising discipline in shaping future research and development activities in academia and industry ranging from engineering, science, finance, economics, arts and humanitarian fields.  New challenges are in modeling of complex systems, sophisticated algorithms, advanced scientific and engineering computing, and associated (multi-disciplinary) problem solving environments.  The papers presented in this volume are specially selected to address the most up-to-date ideas, results, work-in-progress and research experience in the area of high performance computational techniques for science and engineering applications.This state-of-the-are volume presents the proceedings of the International Symposium on High Performance Computational Science and Engineering, held  in conjunction with the IFIP World Computer Congress, August 2004, in Toulouse, France.The collection will be important not only for computational science and engineering experts and researchers but for all teachers and administrators interested in high performance computational techniques.

Markov chains are a particularly powerful and widely used tool for analyzing a variety of stochastic (probabilistic) systems over time. This monograph will present a series of Markov models, starting from the basic models and then building up to higher-order models. Included in the higher-order discussions are multivariate models, higher-order multivariate models, and higher-order hidden models. In each case, the focus is on the important kinds of applications that can be made with the class of models being considered in the current chapter. Special attention is given to numerical algorithms that can efficiently solve the models.Therefore, Markov Chains: Models, Algorithms and Applications outlines recent developments of Markov chain models for modeling queueing sequences, Internet, re-manufacturing systems, reverse logistics, inventory systems, bio-informatics, DNA sequences, genetic networks, data mining, and many other practical systems.

This new edition of Markov Chains: Models, Algorithms and Applications has been completely reformatted as a text, complete with end-of-chapter exercises, a new focus on management science, new applications of the models, and new examples with applications in financial risk management and modeling of financial data.This book consists of eight chapters.  Chapter 1 gives a brief introduction to the classical theory on both discrete and continuous time Markov chains. The relationship between Markov chains of finite states and matrix theory will also be highlighted. Some classical iterative methods for solving linear systems will be introduced for finding the stationary distribution of a Markov chain. The chapter then covers the basic theories and algorithms for hidden Markov models (HMMs) and Markov decision processes (MDPs).Chapter 2 discusses the applications of continuous time Markov chains to model queueing systems and discrete time Markov chain for computing the PageRank, the ranking of websites on the Internet. Chapter 3 studies Markovian models for manufacturing and re-manufacturing systems and presents closed form solutions and fast numerical algorithms for solving the captured systems. In Chapter 4, the authors present a simple hidden Markov model (HMM) with fast numerical algorithms for estimating the model parameters. An application of the HMM for customer classification is also presented. Chapter 5 discusses Markov decision processes for customer lifetime values. Customer Lifetime Values (CLV) is an important concept and quantity in marketing management. The authors present an approach based on Markov decision processes for the calculation of CLV using real data.Chapter 6 considers higher-order Markov chain models, particularly a class of parsimonious higher-order Markov chain models. Efficient estimation methods for model parameters based on linear programming are presented. Contemporary research results on applications to demand predictions, inventory control and financial risk measurement are also presented. In Chapter 7, a class of parsimonious multivariate Markov models is introduced. Again, efficient estimation methods based on linear programming are presented. Applications to demand predictions, inventory control policy and modeling credit ratings data are discussed. Finally, Chapter 8 re-visits hidden Markov models, and the authors present a new class of hidden Markov models with efficient algorithms for estimating the model parameters. Applications to modeling interest rates, credit ratings and default data are discussed. This book is aimed at senior undergraduate students, postgraduate students, professionals, practitioners, and researchers in applied mathematics, computational science, operational research, management science and finance, who are interested in the formulation and computation of queueing networks, Markov chain models and related topics. Readers are expected to have some basic knowledge of probability theory, Markov processes and matrix theory.