Numerical Data Fitting in Dynamical Systems
A Practical Introduction with Applications and Software
Authors: Schittkowski, Klaus
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- About this book
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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.
- Table of contents (5 chapters)
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Introduction
Pages 1-6
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Mathematical Foundations
Pages 7-118
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Data Fitting Models
Pages 119-180
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Numerical Experiments
Pages 181-229
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Case Studies
Pages 231-284
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Table of contents (5 chapters)
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Bibliographic Information
- Bibliographic Information
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- Book Title
- Numerical Data Fitting in Dynamical Systems
- Book Subtitle
- A Practical Introduction with Applications and Software
- Authors
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- Klaus Schittkowski
- Series Title
- Applied Optimization
- Series Volume
- 77
- Copyright
- 2002
- Publisher
- Springer US
- Copyright Holder
- Springer Science+Business Media Dordrecht
- eBook ISBN
- 978-1-4419-5762-7
- DOI
- 10.1007/978-1-4419-5762-7
- Hardcover ISBN
- 978-1-4020-1079-8
- Softcover ISBN
- 978-1-4757-6050-7
- Series ISSN
- 1384-6485
- Edition Number
- 1
- Number of Pages
- XII, 396
- Number of Illustrations
- 42 b/w illustrations
- Topics
