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The Resource Uncertainty Quantification and Stochastic Modeling with Matlab, (electronic book)

Uncertainty Quantification and Stochastic Modeling with Matlab, (electronic book)

Label
Uncertainty Quantification and Stochastic Modeling with Matlab
Title
Uncertainty Quantification and Stochastic Modeling with Matlab
Creator
Contributor
Author
Subject
Language
eng
Summary
Uncertainty Quantification (UQ) is a relatively new research area which describes the methods and approaches used to supply quantitative descriptions of the effects of uncertainty, variability and errors in simulation problems and models. It is rapidly becoming a field of increasing importance, with many real-world applications within statistics, mathematics, probability and engineering, but also within the natural sciences. Literature on the topic has up until now been largely based on polynomial chaos, which raises difficulties when considering different types of approximation and does not lead to a unified presentation of the methods. Moreover, this description does not consider either deterministic problems or infinite dimensional ones. This book gives a unified, practical and comprehensive presentation of the main techniques used for the characterization of the effect of uncertainty on numerical models and on their exploitation in numerical problems. In particular, applications to linear and nonlinear systems of equations, differential equations, optimization and reliability are presented. Applications of stochastic methods to deal with deterministic numerical problems are also discussed. Matlabª illustrates the implementation of these methods and makes the book suitable as a textbook and for self-study
Cataloging source
N$T
http://library.link/vocab/creatorName
Cursi, Eduardo Souza de
Dewey number
519.2
Index
index present
LC call number
QA274.2
Literary form
non fiction
Nature of contents
  • dictionaries
  • bibliography
http://library.link/vocab/relatedWorkOrContributorName
Sampaio, Rubens
http://library.link/vocab/subjectName
  • Stochastic models
  • Uncertainty (Information theory)
  • Stochastic partial differential equations
Label
Uncertainty Quantification and Stochastic Modeling with Matlab, (electronic book)
Instantiates
Publication
Bibliography note
Includes bibliographical references and index
Carrier category
online resource
Carrier category code
  • cr
Carrier MARC source
rdacarrier
Color
multicolored
Content category
text
Content type code
  • txt
Content type MARC source
rdacontent
Contents
  • Front Cover ; Uncertainty Quantification and Stochastic Modeling with Matlab® ; Copyright ; Contents ; Introduction ; Chapter 1: Elements of Probability Theory and Stochastic Processes ; 1.1. Notation ; 1.2. Numerical Characteristics of Finite Populations ; 1.3. Matlab Implementation; 1.4. Couples of Numerical Characteristics ; 1.5. Matlab Implementation ; 1.6. Hilbertian Properties of the Numerical Characteristics ; 1.7. Measure and Probability ; 1.8. Construction of Measures ; 1.9. Measures, Probability and Integrals in Infinite Dimensional Spaces ; 1.10. Random Variables
  • 1.11. Hilbertian Properties of Random Variables 1.12. Sequences of Random Variables ; 1.13. Some Usual Distributions ; 1.14. Samples of Random Variables ; 1.15. Gaussian Samples ; 1.16. Stochastic Processes ; 1.17. Hilbertian Structure ; 1.18. Wiener Process ; 1.19. Ito Integrals ; 1.20. Ito Calculus ; Chapter 2: Maximum Entropy and Information ; 2.1. Construction of a Stochastic Model ; 2.2. The Principle of Maximum Entropy ; 2.3. Generating Samples of Random Variables, Random Vectors and Stochastic Processes
  • 2.4. Karhunen-Loève Expansions and Numerical Generation of Variates from Stochastic Processes Chapter 3: Representation of Random Variables ; 3.1. Approximations Based on Hilbertian Properties ; 3.2. Approximations Based on Statistical Properties (Moment Matching Method); 3.3. Interpolation-Based Approximations (Collocation); Chapter 4: Linear Algebraic Equations Under Uncertainty ; 4.1. Representation of the Solution of Uncertain Linear Systems ; 4.2. Representation of Eigenvalues and Eigenvectors of Uncertain Matrices ; 4.3. Stochastic Methods for Deterministic Linear Systems
  • Chapter 5: Nonlinear Algebraic Equations Involving Random Parameters 5.1. Nonlinear Systems of Algebraic Equations ; 5.2. Numerical Solution of Noisy Deterministic Systems of Nonlinear Equations ; Chapter 6: Differential Equations Under Uncertainty ; 6.1. The Case of Linear Differential Equations ; 6.2. The Case of Nonlinear Differential Equations ; 6.3. The Case of Partial Differential Equations ; 6.4. Reduction of Hamiltonian Systems ; 6.5. Local Solution of Deterministic Differential Equations by Stochastic Simulation ; 6.6. Statistics of Dynamical Systems
  • Chapter 7: Optimization Under Uncertainty 7.1. Representation of the Solutions in Unconstrained Optimization ; 7.2. Stochastic Methods in Deterministic Continuous Optimization ; 7.3. Population-Based Methods; 7.4. Determination of Starting Points ; Chapter 8: Reliability-Based Optimization ; 8.1. The Model Situation ; 8.2. Reliability Index ; 8.3. FORM; 8.4. The Bi-Level or Double-Loop Method; 8.5. One-Level or Single-Loop Approach ; 8.6. Safety Factors ; Bibliography ; Index
Control code
SCIDI906575071
Dimensions
unknown
Extent
1 online resource
File format
unknown
Form of item
online
Isbn
9780081004715
Media category
computer
Media MARC source
rdamedia
Media type code
  • c
Reformatting quality
preservation
Sound
unknown sound
Specific material designation
remote
Label
Uncertainty Quantification and Stochastic Modeling with Matlab, (electronic book)
Publication
Bibliography note
Includes bibliographical references and index
Carrier category
online resource
Carrier category code
  • cr
Carrier MARC source
rdacarrier
Color
multicolored
Content category
text
Content type code
  • txt
Content type MARC source
rdacontent
Contents
  • Front Cover ; Uncertainty Quantification and Stochastic Modeling with Matlab® ; Copyright ; Contents ; Introduction ; Chapter 1: Elements of Probability Theory and Stochastic Processes ; 1.1. Notation ; 1.2. Numerical Characteristics of Finite Populations ; 1.3. Matlab Implementation; 1.4. Couples of Numerical Characteristics ; 1.5. Matlab Implementation ; 1.6. Hilbertian Properties of the Numerical Characteristics ; 1.7. Measure and Probability ; 1.8. Construction of Measures ; 1.9. Measures, Probability and Integrals in Infinite Dimensional Spaces ; 1.10. Random Variables
  • 1.11. Hilbertian Properties of Random Variables 1.12. Sequences of Random Variables ; 1.13. Some Usual Distributions ; 1.14. Samples of Random Variables ; 1.15. Gaussian Samples ; 1.16. Stochastic Processes ; 1.17. Hilbertian Structure ; 1.18. Wiener Process ; 1.19. Ito Integrals ; 1.20. Ito Calculus ; Chapter 2: Maximum Entropy and Information ; 2.1. Construction of a Stochastic Model ; 2.2. The Principle of Maximum Entropy ; 2.3. Generating Samples of Random Variables, Random Vectors and Stochastic Processes
  • 2.4. Karhunen-Loève Expansions and Numerical Generation of Variates from Stochastic Processes Chapter 3: Representation of Random Variables ; 3.1. Approximations Based on Hilbertian Properties ; 3.2. Approximations Based on Statistical Properties (Moment Matching Method); 3.3. Interpolation-Based Approximations (Collocation); Chapter 4: Linear Algebraic Equations Under Uncertainty ; 4.1. Representation of the Solution of Uncertain Linear Systems ; 4.2. Representation of Eigenvalues and Eigenvectors of Uncertain Matrices ; 4.3. Stochastic Methods for Deterministic Linear Systems
  • Chapter 5: Nonlinear Algebraic Equations Involving Random Parameters 5.1. Nonlinear Systems of Algebraic Equations ; 5.2. Numerical Solution of Noisy Deterministic Systems of Nonlinear Equations ; Chapter 6: Differential Equations Under Uncertainty ; 6.1. The Case of Linear Differential Equations ; 6.2. The Case of Nonlinear Differential Equations ; 6.3. The Case of Partial Differential Equations ; 6.4. Reduction of Hamiltonian Systems ; 6.5. Local Solution of Deterministic Differential Equations by Stochastic Simulation ; 6.6. Statistics of Dynamical Systems
  • Chapter 7: Optimization Under Uncertainty 7.1. Representation of the Solutions in Unconstrained Optimization ; 7.2. Stochastic Methods in Deterministic Continuous Optimization ; 7.3. Population-Based Methods; 7.4. Determination of Starting Points ; Chapter 8: Reliability-Based Optimization ; 8.1. The Model Situation ; 8.2. Reliability Index ; 8.3. FORM; 8.4. The Bi-Level or Double-Loop Method; 8.5. One-Level or Single-Loop Approach ; 8.6. Safety Factors ; Bibliography ; Index
Control code
SCIDI906575071
Dimensions
unknown
Extent
1 online resource
File format
unknown
Form of item
online
Isbn
9780081004715
Media category
computer
Media MARC source
rdamedia
Media type code
  • c
Reformatting quality
preservation
Sound
unknown sound
Specific material designation
remote

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