000			06078cam a2200553Ii 4500
001			ocn906575071
003			OCoLC
005			20190328114810.0
006			m o d
007			cr cnu|||unuuu
008			150406s2015 enk ob 001 0 eng d
040			_aN$T _beng _erda _epn _cN$T _dN$T _dBTCTA _dCDX _dCOO _dOPELS _dIDEBK _dE7B _dUIU _dYDXCP _dOCLCF _dEBLCP _dDEBSZ _dFEM _dVGM _dOCLCQ _dBUF _dU3W _dD6H _dOCLCQ _dWYU
019			_a908100355 _a968002077 _a969082919
020			_a9780081004715 _q(electronic bk.)
020			_a0081004710 _q(electronic bk.)
020			_z9781785480058
020			_z1785480057
035			_a(OCoLC)906575071 _z(OCoLC)908100355 _z(OCoLC)968002077 _z(OCoLC)969082919
050		4	_aQA274.2
072		7	_aMAT _x003000 _2bisacsh
072		7	_aMAT _x029000 _2bisacsh
082	0	4	_a519.2 _223
100	1		_aCursi, Eduardo Souza de, _eauthor.
245	1	0	_aUncertainty Quantification and Stochastic Modeling with Matlab / _h[electronic resource]
264		1	_aLondon : _bISTE Press Ltd ; _aKidlington, Oxford : _bElsevier Ltd., _c2015.
300			_a1 online resource
336			_atext _btxt _2rdacontent
337			_acomputer _bc _2rdamedia
338			_aonline resource _bcr _2rdacarrier
347			_atext file _2rda
588	0		_aVendor-supplied metadata.
504			_aIncludes bibliographical references and index.
520			_aUncertainty 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.
505	0		_aFront 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.
505	8		_a1.11. 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.
505	8		_a2.4. 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.
505	8		_aChapter 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.
505	8		_aChapter 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.
650		0	_aStochastic models.
650		0	_aUncertainty (Information theory)
650		7	_aMATHEMATICS _xApplied. _2bisacsh
650		7	_aMATHEMATICS _xProbability & Statistics _xGeneral. _2bisacsh
650		7	_aStochastic models. _2fast _0(OCoLC)fst01737780
650		7	_aUncertainty (Information theory) _2fast _0(OCoLC)fst01160838
655		4	_aElectronic books.
700	1		_aSampaio, Rubens, _eauthor.
776	0	8	_iPrint version: _z9780081004715 _w(OCoLC)906575071
856	4	0	_3ScienceDirect _uhttp://www.sciencedirect.com/science/book/9781785480058
999			_c247068 _d247068