Ferenc Szidarovszky - Böcker

It is an incontestable fact that numerical analysis techniques are used rou­ tinely (although not always effectively) in virtually every quantitative field of scientific endeavor. In this book, which is directed toward upper-division and graduate level students in engineering and mathematics, we have selected for discussion subjects that are traditionally found in numerical analysis texts. But our choice of methodology rejects the traditional where analysis and experience clearly warrant such a departure, and one of our primary aspirations in this work is to equip the reader with the wherewithal to apply numerical analysis thinking to nontraditional subjects. For there is a plethora of computer-oriented sciences such as optimization, statistics, and system analysis and identification that are sorely in need of methods comparable to those related here for classical numerical analysis problems. Toward uncovering for the reader the structure of numerical methods we have, for example, devoted a chapter to a metric space theory for iter­ ative application of operators. In this chapter, we have collected those definitions and concepts of real and functional analysis that are requisite to a modern intermediate-level exposition of the principles of numerical anal­ ysis. Further, we derive the abstract theory (most notably, the contraction mapping theorem) for iteration processes.

Game theory, defined in the broadest sense, is a collection of mathematical models designed for the analysis of strategic aspects of situations of conflict and cooperation in a broad spectrum of fields including economics, politics, biology, engineering, and operations research. This book, besides covering the classical results of game theory, places special emphasis on methods of determining "solutions" of various game models. Generalizations reaching beyond the "convexity paradigm" and leading to nonconvex optimization problems are enhanced and discussed in more detail than in standard texts on this subject. The development is theoretical-mathematical interspersed with elucidating interpretations and examples.

Writing in honour of Sid Yakowitz, 50 internationally known scholars have collectively contributed 30 papers on modelling uncertainty to this volume. The papers cover a variety of topics such as probability, statistics, economics, stochastic optimization, control theory, regression analysis, simulation, stochastic programming, Markov decision process and application in the HIV context. There are papers with a theoretical emphasis and others that focus on applications. A number of papers survey the work in a particular area and in a few papers the authors present their personal view of a topic. It is a book with a considerable number of expository articles, which are accessible to a nonexpert - a graduate student in mathematics, statistics, engineering and economics departments, or anyone with some mathematical background who is interested in a preliminary exposition of a particular topic. Many of the papers present the state of the art of a specific area or represent original contributions which advance the present state of knowledge.

This second edition comprehensively presents important tools of linear systems theory, including differential and difference equations, Laplace and Z transforms, and more.Linear Systems Theory discusses:Nonlinear and linear systems in the state space form and through the transfer function method Stability, including marginal stability, asymptotical stability, global asymptotical stability, uniform stability, uniform exponential stability, and BIBO stability Controllability Observability Canonical forms System realizations and minimal realizations, including state space approach and transfer function realizations System design Kalman filters Nonnegative systems Adaptive control Neural networksThe book focuses mainly on applications in electrical engineering, but it provides examples for most branches of engineering, economics, and social sciences.What's New in the Second Edition? Case studies drawn mainly from electrical and mechanical engineering applications, replacing many of the longer case studies Expanded explanations of both linear and nonlinear systems as well as new problem sets at the end of each chapter Illustrative examples in all the chapters An introduction and analysis of new stability concepts An expanded chapter on neural networks, analyzing advances that have occurred in that field since the first editionAlthough more mainstream than its predecessor, this revision maintains the rigorous mathematical approach of the first edition, providing fast, efficient development of the material.Linear Systems Theory enables its reader to develop his or her capabilities for modeling dynamic phenomena, examining their properties, and applying them to real-life situations.

The Theory and Applications of Iteration Methods focuses on an abstract iteration scheme that consists of the recursive application of a point-to-set mapping. Each chapter presents new theoretical results and important applications in engineering, dynamic economic systems, and input-output systems. At the end of each chapter, case studies and numerical examples are presented from different fields of engineering and economics. Following an outline of general iteration schemes, the authors extend the discrete time-scale Liapunov theory to time-dependent, higher order, nonlinear difference equations. The monotone convergence to the solution is examined in and comparison theorems are proven . Results generalize well-known classical theorems, such as the contraction mapping principle, the lemma of Kantorovich, the famous Gronwall lemma, and the stability theorem of Uzawa. The book explores conditions for the convergence of special single- and two-step methods such as Newton's method, modified Newton's method, and Newton-like methods generated by point-to-point mappings in a Banach space setting. Conditions are examined for monotone convergence of Newton's methods and their variants. Students and professionals in engineering, the physical sciences, mathematics, and economics will benefit from the book's detailed examples, step-by-step explanations, and effective organization.

A comprehensive guide to the application and processing of condition-based data to produce prognostic estimates of functional health and life. Prognostics and Health Management provides an authoritative guide for an understanding of the rationale and methodologies of a practical approach for improving system reliability using conditioned-based data (CBD) to the monitoring and management of health of systems. This proven approach uses electronic signatures extracted from conditioned-based electrical signals, including those representing physical components, and employs processing methods that include data fusion and transformation, domain transformation, and normalization, canonicalization and signal-level translation to support the determination of predictive diagnostics and prognostics. Written by noted experts in the field, Prognostics and Health Management clearly describes how to extract signatures from conditioned-based data using conditioning methods such as data fusion and transformation, domain transformation, data type transformation and indirect and differential comparison. This important resource: Integrates data collecting, mathematical modelling and reliability prediction in one volumeContains numerical examples and problems with solutions that help with an understanding of the algorithmic elements and processesPresents information from a panel of experts on the topicFollows prognostics based on statistical modelling, reliability modelling and usage modelling methodsWritten for system engineers working in critical process industries and automotive and aerospace designers, Prognostics and Health Management offers a guide to the application of condition-based data to produce signatures for input to predictive algorithms to produce prognostic estimates of functional health and life.

Game theory, defined in the broadest sense, is a collection of mathematical models designed for the analysis of strategic aspects of situations of conflict and cooperation in a broad spectrum of fields including economics, politics, biology, engineering, and operations research. This book, besides covering the classical results of game theory, places special emphasis on methods of determining `solutions' of various game models. Generalizations reaching beyond the `convexity paradigm' and leading to nonconvex optimization problems are enhanced and discussed in more detail than in standard texts on this subject. The development is theoretical-mathematical interspersed with elucidating interpretations and examples. Audience: The material in the book is accessible to PhD and graduate students and will also be of interest to researchers. Solid knowledge of standard undergraduate mathematics is required to read the book.

The papers cover a great variety of topics in probability, statistics, economics, stochastic optimization, control theory, regression analysis, simulation, stochastic programming, Markov decision process, application in the HIV context, and others.

Focusing on conflict resolution, Water Resources Systems Analysis discusses systematic approaches to the mathematical modeling of various water resources issues, which helps decision-makers allocate water effectively and efficiently. Readers will gain an understanding of simulation, optimization, multi-criterion-decision-making, as well as engineering economics and time series analysis, all necessary for successful water systems analysis. The book explores recent developments in surface and groundwater systems optimization and modeling, and it relates these to real field applications and case studies. Supported by essential mathematical tools, this book gives current and future hydrologists, water resources managers, and civil engineers a logical reference for prioritizing and addressing critical issues such as flood control, power generation, and water quality management.

Oligopoly theory is one of the most intensively studied areas of mathematical economics. On the basis of the pioneering works of Cournot (1838), many res- rchers have developed and extensively examined the different variants of oligopoly models. Initially, the existence and uniqueness of the equilibrium of the different types of oligopolies was the main concern, and later the dynamic extensions of these models became the focus. The classical result of Theocharis (1960) asserts that under discrete time scales and static expectations, the equilibrium of a sing- product oligopoly without product differentiation and with linear price and cost functions is asymptotically stable if and only if it is a duopoly. In the continuous time case, asymptotic stability is guaranteed for any number of ?rms. In these cases the resulting dynamical systems are also linear, where local and global asymptotic stability are equivalent to each other. The classical book of Okuguchi (1976) gives a comprehensive summary of the earlier results and developments.The multipr- uct extensionshave been discussed in Okuguchiand Szidarovszky(1999);however, nonlinear features were barely touched upon in these contributions. WiththedevelopmentofthecriticalcurvemethodbyGumowskiandMira(1980) (see also Mira et al. (1996))fordiscrete time systemsand the introductionof cont- uously distributed information lags by Invernizzi and Medio (1991) in continuous time systems, increasing attention has been given to the global dynamics of n- linear oligopolies. The authors of this book have devoted a great deal of research effort to this area.

Multicriteria analysis is one of the most important fields of decision science. This book gives an outline of the formulation of an appropriate model and presents a comprehensive summary of the most popular methods for solving multicriteria decision problems. In addition to the classical approach the book introduces fuzzy and stochastic methodology, models with uncertainty, social choice and conflict resolution. All methods are illustrated with easy to follow simple examples. At the end of each chapter detailed case studies are given in water and environment management including inter-basin water transfer, urban water management, water allocation, groundwater quality management, forest treatment, ranking water resources projects, reservoir planning, water distribution network design and long-term watershed management. The new methodology and the wide variety of case studies are not easily accessible elsewhere.

Oligopoly theory is one of the most intensively studied areas of mathematical economics. On the basis of the pioneering works of Cournot (1838), many res- rchers have developed and extensively examined the different variants of oligopoly models. Initially, the existence and uniqueness of the equilibrium of the different types of oligopolies was the main concern, and later the dynamic extensions of these models became the focus. The classical result of Theocharis (1960) asserts that under discrete time scales and static expectations, the equilibrium of a sing- product oligopoly without product differentiation and with linear price and cost functions is asymptotically stable if and only if it is a duopoly. In the continuous time case, asymptotic stability is guaranteed for any number of ?rms. In these cases the resulting dynamical systems are also linear, where local and global asymptotic stability are equivalent to each other. The classical book of Okuguchi (1976) gives a comprehensive summary of the earlier results and developments.The multipr- uct extensionshave been discussed in Okuguchiand Szidarovszky(1999);however, nonlinear features were barely touched upon in these contributions. WiththedevelopmentofthecriticalcurvemethodbyGumowskiandMira(1980) (see also Mira et al. (1996))fordiscrete time systemsand the introductionof cont- uously distributed information lags by Invernizzi and Medio (1991) in continuous time systems, increasing attention has been given to the global dynamics of n- linear oligopolies. The authors of this book have devoted a great deal of research effort to this area.

Multicriteria analysis is one of the most important fields of decision science. This book gives an outline of the formulation of an appropriate model and presents a comprehensive summary of the most popular methods for solving multicriteria decision problems. In addition to the classical approach the book introduces fuzzy and stochastic methodology, models with uncertainty, social choice and conflict resolution. All methods are illustrated with easy to follow simple examples. At the end of each chapter detailed case studies are given in water and environment management including inter-basin water transfer, urban water management, water allocation, groundwater quality management, forest treatment, ranking water resources projects, reservoir planning, water distribution network design and long-term watershed management. The new methodology and the wide variety of case studies are not easily accessible elsewhere.

In the mid 1960's both authors undertook independent works in oligopoly.and game theory. However, it was not until 1983 that they formally met. Since then, they have continued meeting either in Budapest or Tokyo. Their collaboration has resulted in numerous publications as well as in this work. Essentially, this book has two origins. First, it originated in previous results, either published or circulated in mimeograph form. Finely sifting their results, the authors constructed a concise reinterpretation of their achievement to date. However, this unifying process led to the second origin. Reconsideration, particularly in this comprehensive approach, generated new results. This was especially true in the analysis of the existence, uniqueness and global stability of the Cournot-Nash equilibrium for oligopoly with multi-product flrms, and for several modilled Cournot and related models. This book should be ideal for graduate students in economics or mathematics. However, as the authors have firmly grounded their ideas in the formal language of mathematics, the student should possess some background in calculus, linear algebra, and ordinary differential and difference equations. Additionally, the book should be useful to researchers in oligopoly and game theory as well as to mathematically oriented economists. The methodology developed for analyzing the existence and stability of oligopoly equilibrium should prove useful also in theoretical analysis of other economic models. Weare both very grateful to Professor Wilhelm Krelle for his careful review and helpful suggestions. In addition, Koji Okuguchi wishes to thank Professors W.

This book integrates the fundamentals, methodology, and major application fields of noncooperative and cooperative games including conflict resolution. The topics addressed in the book are discrete and continuous games including games represented by finite trees; matrix and bimatrix games as well as oligopolies; cooperative solution concepts; games under uncertainty; dynamic games and conflict resolution. The methodology is illustrated by carefully chosen examples, applications and case studies which are selected from economics, social sciences, engineering, the military and homeland security. This book is highly recommended to readers who are interested in the in-depth and up-to-date integration of the theory and ever-expanding application areas of game theory.

This book integrates the fundamentals, methodology, and major application fields of noncooperative and cooperative games including conflict resolution. The topics addressed in the book are discrete and continuous games including games represented by finite trees;

In economic modeling and planning, as well as in business, most problems are linear, or approximated by linear models. Such problems are solved by matrix methods, so the material presented in this book is essential to these fields.

In economic modeling and planning, as well as in business, most problems are linear, or approximated by linear models. Such problems are solved by matrix methods, so the material presented in this book is essential to these fields.

This book reflects the state of the art in nonlinear economic dynamics, providing a broad overview of dynamic economic models at different levels. The wide variety of approaches ranges from theoretical and simulation analysis to methodological study. In particular, it examines the local and global asymptotical behavior of both macro- and micro- level mathematical models, theoretically as well as using simulation. It also focuses on systems with one or more time delays for which new methodology has to be developed to investigate their asymptotic properties. The book offers a comprehensive summary of the existing methodology with extensions to the more complex model variants, since considerations on bounded rationality of complex economic behavior provide the foundation underlying choice-theoretic and policy-oriented studies of macro behavior, which impact the real macro economy. It includes 13 chapters addressing traditional models such as monopoly, duopoly and oligopoly in microeconomics and Keynesian, Goodwinian, and Kaldor–Kaleckian models in macroeconomics. Each chapter presents new aspects of these traditional models that have never been seen before. This work renews the past wisdom and reveals tomorrow's knowledge.

This book reflects the state of the art in nonlinear economic dynamics, providing a broad overview of dynamic economic models at different levels.

Linear algebra and matrix theory are among the most important and most frequently applied branches of mathematics. They are especially important in solving engineering and economic models, where either the model is assumed linear, or the nonlinear model is approximated by a linear model, and the resulting linear model is examined.This book is mainly a textbook, that covers a one semester upper division course or a two semester lower division course on the subject.The second edition will be an extended and modernized version of the first edition. We added some new theoretical topics and some new applications from fields other than economics. We also added more difficult exercises at the end of each chapter which require deep understanding of the theoretical issues. We also modernized some proofs in the theoretical discussions which give better overview of the study material. In preparing the manuscript we also corrected the typos and errors, so the second edition will be a corrected, extended and modernized new version of the first edition.

Linear algebra and matrix theory are among the most important and most frequently applied branches of mathematics. They are especially important in solving engineering and economic models, where either the model is assumed linear, or the nonlinear model is approximated by a linear model, and the resulting linear model is examined.This book is mainly a textbook, that covers a one semester upper division course or a two semester lower division course on the subject.The second edition will be an extended and modernized version of the first edition. We added some new theoretical topics and some new applications from fields other than economics. We also added more difficult exercises at the end of each chapter which require deep understanding of the theoretical issues. We also modernized some proofs in the theoretical discussions which give better overview of the study material. In preparing the manuscript we also corrected the typos and errors, so the second edition will be a corrected, extended and modernized new version of the first edition.

This is the first book to comprehensively examine the asymptotic behavior of dynamic monopolies, duopolies, and oligopolies where firms face information and implementation delays.

The respective chapters cover a range of theoretical issues and examples concerning how the qualitative theory of dynamical systems is used to analyze the local and global bifurcations that characterize complex behaviors observed in social systems where heterogeneous and boundedly rational economic agents interact.

The respective chapters cover a range of theoretical issues and examples concerning how the qualitative theory of dynamical systems is used to analyze the local and global bifurcations that characterize complex behaviors observed in social systems where heterogeneous and boundedly rational economic agents interact.