Numerical Data Fitting In Dynamical Systems
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Numerical Data Fitting In Dynamical Systems
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Author : Klaus Schittkowski
language : en
Publisher: Springer
Release Date : 2002-12-31
Numerical Data Fitting In Dynamical Systems written by Klaus Schittkowski and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2002-12-31 with Computers categories.
Real life phenomena in engineering, natural, or medical sciences are often described by a mathematical model with the goal to analyze numerically the behaviour of the system. Advantages of mathematical models are their cheap availability, the possibility of studying extreme situations that cannot be handled by experiments, or of simulating real systems during the design phase before constructing a first prototype. Moreover, they serve to verify decisions, to avoid expensive and time consuming experimental tests, to analyze, understand, and explain the behaviour of systems, or to optimize design and production. As soon as a mathematical model contains differential dependencies from an additional parameter, typically the time, we call it a dynamical model. There are two key questions always arising in a practical environment: 1 Is the mathematical model correct? 2 How can I quantify model parameters that cannot be measured directly? In principle, both questions are easily answered as soon as some experimental data are available. The idea is to compare measured data with predicted model function values and to minimize the differences over the whole parameter space. We have to reject a model if we are unable to find a reasonably accurate fit. To summarize, parameter estimation or data fitting, respectively, is extremely important in all practical situations, where a mathematical model and corresponding experimental data are available to describe the behaviour of a dynamical system.
Numerical Data Fitting In Dynamical Systems
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Author : Klaus Schittkowski
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-06-05
Numerical Data Fitting In Dynamical Systems written by Klaus Schittkowski and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-06-05 with Mathematics categories.
Real life phenomena in engineering, natural, or medical sciences are often described by a mathematical model with the goal to analyze numerically the behaviour of the system. Advantages of mathematical models are their cheap availability, the possibility of studying extreme situations that cannot be handled by experiments, or of simulating real systems during the design phase before constructing a first prototype. Moreover, they serve to verify decisions, to avoid expensive and time consuming experimental tests, to analyze, understand, and explain the behaviour of systems, or to optimize design and production. As soon as a mathematical model contains differential dependencies from an additional parameter, typically the time, we call it a dynamical model. There are two key questions always arising in a practical environment: 1 Is the mathematical model correct? 2 How can I quantify model parameters that cannot be measured directly? In principle, both questions are easily answered as soon as some experimental data are available. The idea is to compare measured data with predicted model function values and to minimize the differences over the whole parameter space. We have to reject a model if we are unable to find a reasonably accurate fit. To summarize, parameter estimation or data fitting, respectively, is extremely important in all practical situations, where a mathematical model and corresponding experimental data are available to describe the behaviour of a dynamical system.
Numerical Data Fitting In Dynamical Systems
DOWNLOAD
Author : Klaus Schittkowski
language : en
Publisher: Springer Science & Business Media
Release Date : 2002-12-31
Numerical Data Fitting In Dynamical Systems written by Klaus Schittkowski and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2002-12-31 with Computers categories.
Real life phenomena in engineering, natural, or medical sciences are often described by a mathematical model with the goal to analyze numerically the behaviour of the system. Advantages of mathematical models are their cheap availability, the possibility of studying extreme situations that cannot be handled by experiments, or of simulating real systems during the design phase before constructing a first prototype. Moreover, they serve to verify decisions, to avoid expensive and time consuming experimental tests, to analyze, understand, and explain the behaviour of systems, or to optimize design and production. As soon as a mathematical model contains differential dependencies from an additional parameter, typically the time, we call it a dynamical model. There are two key questions always arising in a practical environment: 1 Is the mathematical model correct? 2 How can I quantify model parameters that cannot be measured directly? In principle, both questions are easily answered as soon as some experimental data are available. The idea is to compare measured data with predicted model function values and to minimize the differences over the whole parameter space. We have to reject a model if we are unable to find a reasonably accurate fit. To summarize, parameter estimation or data fitting, respectively, is extremely important in all practical situations, where a mathematical model and corresponding experimental data are available to describe the behaviour of a dynamical system.
Practical Methods For Optimal Control Using Nonlinear Programming Third Edition
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Author : John T. Betts
language : en
Publisher: SIAM
Release Date : 2020-07-09
Practical Methods For Optimal Control Using Nonlinear Programming Third Edition written by John T. Betts and has been published by SIAM this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-07-09 with Mathematics categories.
How do you fly an airplane from one point to another as fast as possible? What is the best way to administer a vaccine to fight the harmful effects of disease? What is the most efficient way to produce a chemical substance? This book presents practical methods for solving real optimal control problems such as these. Practical Methods for Optimal Control Using Nonlinear Programming, Third Edition focuses on the direct transcription method for optimal control. It features a summary of relevant material in constrained optimization, including nonlinear programming; discretization techniques appropriate for ordinary differential equations and differential-algebraic equations; and several examples and descriptions of computational algorithm formulations that implement this discretize-then-optimize strategy. The third edition has been thoroughly updated and includes new material on implicit Runge–Kutta discretization techniques, new chapters on partial differential equations and delay equations, and more than 70 test problems and open source FORTRAN code for all of the problems. This book will be valuable for academic and industrial research and development in optimal control theory and applications. It is appropriate as a primary or supplementary text for advanced undergraduate and graduate students.
Dynamic Data Analysis
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Author : James Ramsay
language : en
Publisher: Springer
Release Date : 2017-06-27
Dynamic Data Analysis written by James Ramsay and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-06-27 with Mathematics categories.
This text focuses on the use of smoothing methods for developing and estimating differential equations following recent developments in functional data analysis and building on techniques described in Ramsay and Silverman (2005) Functional Data Analysis. The central concept of a dynamical system as a buffer that translates sudden changes in input into smooth controlled output responses has led to applications of previously analyzed data, opening up entirely new opportunities for dynamical systems. The technical level has been kept low so that those with little or no exposure to differential equations as modeling objects can be brought into this data analysis landscape. There are already many texts on the mathematical properties of ordinary differential equations, or dynamic models, and there is a large literature distributed over many fields on models for real world processes consisting of differential equations. However, a researcher interested in fitting such a model to data, or a statistician interested in the properties of differential equations estimated from data will find rather less to work with. This book fills that gap.
From Nano To Space
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Author : Michael Breitner
language : en
Publisher: Springer Science & Business Media
Release Date : 2007-11-04
From Nano To Space written by Michael Breitner and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007-11-04 with Mathematics categories.
This book shows how modern Applied Mathematics influences everyday life. It features contributors from universities, research institutions and industry, who combine research and review papers to present a survey of current research. More than 20 contributions are divided into scales: nano, micro, macro, space and real life. In addition, coverage includes engaging and informative case studies as well as complex graphics and illustrations, many of them in color.
Analytical Methods For Dynamic Modelers
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Author : Hazhir Rahmandad
language : en
Publisher: MIT Press
Release Date : 2015-11-13
Analytical Methods For Dynamic Modelers written by Hazhir Rahmandad and has been published by MIT Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-11-13 with Business & Economics categories.
A user-friendly introduction to some of the most useful analytical tools for model building, estimation, and analysis, presenting key methods and examples. Simulation modeling is increasingly integrated into research and policy analysis of complex sociotechnical systems in a variety of domains. Model-based analysis and policy design inform a range of applications in fields from economics to engineering to health care. This book offers a hands-on introduction to key analytical methods for dynamic modeling. Bringing together tools and methodologies from fields as diverse as computational statistics, econometrics, and operations research in a single text, the book can be used for graduate-level courses and as a reference for dynamic modelers who want to expand their methodological toolbox. The focus is on quantitative techniques for use by dynamic modelers during model construction and analysis, and the material presented is accessible to readers with a background in college-level calculus and statistics. Each chapter describes a key method, presenting an introduction that emphasizes the basic intuition behind each method, tutorial style examples, references to key literature, and exercises. The chapter authors are all experts in the tools and methods they present. The book covers estimation of model parameters using quantitative data; understanding the links between model structure and its behavior; and decision support and optimization. An online appendix offers computer code for applications, models, and solutions to exercises. Contributors Wenyi An, Edward G. Anderson Jr., Yaman Barlas, Nishesh Chalise, Robert Eberlein, Hamed Ghoddusi, Winfried Grassmann, Peter S. Hovmand, Mohammad S. Jalali, Nitin Joglekar, David Keith, Juxin Liu, Erling Moxnes, Rogelio Oliva, Nathaniel D. Osgood, Hazhir Rahmandad, Raymond Spiteri, John Sterman, Jeroen Struben, Burcu Tan, Karen Yee, Gönenç Yücel
Optimization And Operations Research Volume I
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Author : Ulrich Derigs
language : en
Publisher: EOLSS Publications
Release Date : 2009-02-09
Optimization And Operations Research Volume I written by Ulrich Derigs and has been published by EOLSS Publications this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009-02-09 with categories.
Optimization and Operations Research is a component of Encyclopedia of Mathematical Sciences in the global Encyclopedia of Life Support Systems (EOLSS), which is an integrated compendium of twenty one Encyclopedias. The Theme on Optimization and Operations Research is organized into six different topics which represent the main scientific areas of the theme: 1. Fundamentals of Operations Research; 2. Advanced Deterministic Operations Research; 3. Optimization in Infinite Dimensions; 4. Game Theory; 5. Stochastic Operations Research; 6. Decision Analysis, which are then expanded into multiple subtopics, each as a chapter. These four volumes are aimed at the following five major target audiences: University and College students Educators, Professional Practitioners, Research Personnel and Policy Analysts, Managers, and Decision Makers and NGOs.
Scaling Laws In Dynamical Systems
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Author : Edson Denis Leonel
language : en
Publisher: Springer Nature
Release Date : 2021-08-26
Scaling Laws In Dynamical Systems written by Edson Denis Leonel and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-08-26 with Mathematics categories.
This book discusses many of the common scaling properties observed in some nonlinear dynamical systems mostly described by mappings. The unpredictability of the time evolution of two nearby initial conditions in the phase space together with the exponential divergence from each other as time goes by lead to the concept of chaos. Some of the observables in nonlinear systems exhibit characteristics of scaling invariance being then described via scaling laws. From the variation of control parameters, physical observables in the phase space may be characterized by using power laws that many times yield into universal behavior. The application of such a formalism has been well accepted in the scientific community of nonlinear dynamics. Therefore I had in mind when writing this book was to bring together few of the research results in nonlinear systems using scaling formalism that could treated either in under-graduation as well as in the post graduation in the several exact programs but no earlier requirements were needed from the students unless the basic physics and mathematics. At the same time, the book must be original enough to contribute to the existing literature but with no excessive superposition of the topics already dealt with in other text books. The majority of the Chapters present a list of exercises. Some of them are analytic and others are numeric with few presenting some degree of computational complexity.
Computational Methods In Systems Biology
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Author : Pierpaolo Degano
language : en
Publisher: Springer
Release Date : 2009-08-27
Computational Methods In Systems Biology written by Pierpaolo Degano and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009-08-27 with Science categories.
This volume contains the proceedings of the 7th Conference on Computational Methods in Systems Biology (CMSB 2009), held in Bologna, from August 31 to September 1, 2009. The ?rst CMSB was held in Trento in 2003, bringing together life scientists, computer scientists, engineers and physicists. The goal was to promote the c- vergence of di?erent disciplines aiming at a new understanding and description of biological systems, ?rmly ground in formal models, supported by compu- tionallanguagesandtools,ando?eringnew methodsofanalysis.The conference then moved to Paris in 2004, Edinburgh in 2005, Trento in 2006, Edinburgh in 2007 and Rostock/Warnemunde ̈ in 2008. This year the conference attracted about 45 submissions form 18 countries, mainly from Europe and North America, but also from Asia and Australia. We wish to thank all authors for their interest in CMSB 2009. After careful disc- sions, the Programme Committee eventually selected 18 papers for presentation at the conference. Each of them was accurately refereed by at least three - viewers, who delivered detailed and insightful comments and suggestions. The Conference Chairmen warmly thank all the members of the Programme C- mittee and all their sub-referees for the excellent support they gave, as well as for the friendly and constructive discussions. We also would like to thank the authorsfor havingrevisedtheir papers to addressthe comments andsuggestions by the referees.