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In this book, we study theoretical and practical aspects of computing methods for mathematical modelling of nonlinear systems. A number of computing techniques are considered, such as methods of operator approximation with any given accuracy; operator interpolation techniques including a non-Lagrange interpolation; methods of system representation subject to constraints associated with concepts of causality, memory and stationarity; methods of system representation with an accuracy that is the best within a given class of models; methods of covariance matrix estimation;methods for low-rank

Search theory. --- Operations research. --- Operational analysis --- Operational research --- Industrial engineering --- Management science --- Research --- System theory --- Operations research --- Search theory --- 519.8 --- 519.8 Operational research

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This book begins with a review of basic results in optimal search for a stationary target. It then develops the theory of optimal search for a moving target, providing algorithms for computing optimal plans and examples of their use. Next it develops methods for computing optimal search plans involving multiple targets and multiple searchers with realistic operational constraints on search movement. These results assume that the target does not react to the search. In the final chapter there is a brief overview of mostly military problems where the target tries to avoid being found as well as rescue or rendezvous problems where the target and the searcher cooperate. Larry Stone wrote his definitive book Theory of Optimal Search in 1975, dealing almost exclusively with the stationary target search problem. Since then the theory has advanced to encompass search for targets that move even as the search proceeds, and computers have developed sufficient capability to employ the improved theory. In this book, Stone joins Royset and Washburn to document and explain this expanded theory of search. The problem of how to search for moving targets arises every day in military, rescue, law enforcement, and border patrol operations. .

Business. --- Market research. --- Operations research. --- Decision making. --- Management science. --- Business and Management. --- Operation Research/Decision Theory. --- Operations Research, Management Science. --- Market Research/Competitive Intelligence. --- Industrial management --- Production management --- Search theory. --- Research. --- Operational analysis --- Operational research --- Manufacturing management --- Industrial engineering --- Management science --- Research --- System theory --- Operations research --- Operations Research/Decision Theory. --- Market research --- Marketing --- Markets --- Research, Industrial --- Quantitative business analysis --- Management --- Problem solving --- Statistical decision --- Deciding --- Decision (Psychology) --- Decision analysis --- Decision processes --- Making decisions --- Management decisions --- Choice (Psychology) --- Decision making

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This book provides a quick but insightful introduction to Bayesian tracking and particle filtering for a person who has some background in probability and statistics and wishes to learn the basics of single-target tracking. It also introduces the reader to multiple target tracking by presenting useful approximate methods that are easy to implement compared to full-blown multiple target trackers. The book presents the basic concepts of Bayesian inference and demonstrates the power of the Bayesian method through numerous applications of particle filters to tracking and smoothing problems. It emphasizes target motion models that incorporate knowledge about the target’s behavior in a natural fashion rather than assumptions made for mathematical convenience. The background provided by this book allows a person to quickly become a productive member of a project team using Bayesian filtering and to develop new methods and techniques for problems the team may face.

Statistical science --- Mathematical statistics --- Information systems --- statistiek --- gegevensanalyse --- Engineering—Data processing. --- Statistics. --- Big data. --- Data Engineering. --- Bayesian Inference. --- Big Data. --- Mathematics