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Numerical Data Fitting in Dynamical Systems: A Practical Introduction with Applications and Software: 77 (Applied Optimization) - Tapa dura
Reseña del editor:
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.
Reseña del editor:
The main objective of the book is to give an overview of numerical methods to compute parameters of a dynamical model by a least squares fit of experimental data. The mathematical equations under consideration are explicit model functions or steady state systems in the simplest case, or responses of dynamical systems defined by ordinary differential equations, differential algebraic equations, partial differential equations, and partial differential algebraic equations (1D). Many different mathematical disciplines must be combined to find a solution, for example nonlinear programming, least squares optimization, systems of nonlinear equations, ordinary differential equations, discretization of partial differential equations, sensitivity analysis, automatic differentiation, and statistics.
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- EditorialSpringer
- Año de publicación2002
- ISBN 10 1402010796
- ISBN 13 9781402010798
- EncuadernaciónTapa dura
- Número de páginas396
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NUMERICAL DATA FITTING IN DYNAMI
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ISBN 13: 9781402010798
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Numerical Data Fitting in Dynamical Systems
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ISBN 10: 1402010796
ISBN 13: 9781402010798
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Descripción Condición: New. Dieser Artikel ist ein Print on Demand Artikel und wird nach Ihrer Bestellung fuer Sie gedruckt. 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. Nº de ref. del artículo: 4092323
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Numerical Data Fitting in Dynamical Systems
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Springer US Dez 2002
(2002)
ISBN 10: 1402010796
ISBN 13: 9781402010798
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Descripción Buch. Condición: Neu. This item is printed on demand - it takes 3-4 days longer - Neuware -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. 412 pp. Englisch. Nº de ref. del artículo: 9781402010798
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Numerical Data Fitting in Dynamical Systems : A Practical Introduction with Applications and Software
Publicado por
Springer US
(2002)
ISBN 10: 1402010796
ISBN 13: 9781402010798
Nuevo
Tapa dura
Cantidad disponible: 1
Librería:
Valoración
Descripción Buch. Condición: Neu. Druck auf Anfrage Neuware - Printed after ordering - 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. Nº de ref. del artículo: 9781402010798
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