06078cam a2200553Ii 4500 ocn906575071 OCoLC 20190328114810.0 m o d cr cnu|||unuuu 150406s2015 enk ob 001 0 eng d N$T eng rda pn N$T N$T BTCTA CDX COO OPELS IDEBK E7B UIU YDXCP OCLCF EBLCP DEBSZ FEM VGM OCLCQ BUF U3W D6H OCLCQ WYU 908100355 968002077 969082919 9780081004715 (electronic bk.) 0081004710 (electronic bk.) 9781785480058 1785480057 (OCoLC)906575071 (OCoLC)908100355 (OCoLC)968002077 (OCoLC)969082919 QA274.2 MAT 003000 bisacsh MAT 029000 bisacsh 519.2 23 Cursi, Eduardo Souza de, author. Uncertainty Quantification and Stochastic Modeling with Matlab / [electronic resource] London : ISTE Press Ltd ; Kidlington, Oxford : Elsevier Ltd., 2015. 1 online resource text txt rdacontent computer c rdamedia online resource cr rdacarrier text file rda Vendor-supplied metadata. Includes bibliographical references and index. 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. Matlab� illustrates the implementation of these methods and makes the book suitable as a textbook and for self-study. 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-Lo�eve 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. Stochastic models. Uncertainty (Information theory) MATHEMATICS Applied. bisacsh MATHEMATICS Probability & Statistics General. bisacsh Stochastic models. fast (OCoLC)fst01737780 Uncertainty (Information theory) fast (OCoLC)fst01160838 Electronic books. Sampaio, Rubens, author. Print version: 9780081004715 (OCoLC)906575071 ScienceDirect http://www.sciencedirect.com/science/book/9781785480058 247068 247068