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Polynomial Chaos Methods
Uncertainty quantification becomes a more and more important task in many applications. BERGISCHE UNIVERSITÄT WUPPERTAL :: FB C :: NUMERISCHE MATHEMATIK : : Polynomial Chaos
UQ - YouQ YouQ: A self-guided tour of Uncertainty Quantification This page provides references and links to introductory material on UQ and to computational tools that are freely available on the Web. Uncertainty Quantification: what is it?
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Uncertainty Quantification Overview The rapid growth of high-performance supercomputing technology and advances in numerical techniques in the last two decades have provided an unprecedented opportunity to explore complex physical phenomena using modeling and simulation.
Sparse Grid Interpolation Toolbox Sparse Grid Interpolation Toolbox The Sparse Grid Interpolation Toolbox is a Matlab toolbox for recovering (approximating) expensive, possibly high-dimensional multivariate functions. It was developed by Andreas Klimke at the Institute of Applied Analysis and Numerical Simulation at the High Performance Scientific Computing lab ("Lehrstuhl für Numerische Mathematik für Höchstleistungsrechner"), Universität Stuttgart during his Ph.D. studies.
Introduction to Uncertainty Quantification Gianluca Iaccarino, Stanford University
UQ - Home "If a man will begin with certainties, he shall end in doubts; but if he will be content to begin with doubts, he shall end in certainties." - F. Bacon - 1605.
ME470 | Uncertainty Quantification | Stanford University
Imprecise Probability Propagation Toolbox for Matlab Current version: 1.0 What is IPP Toolbox? The IPP Toolbox is a collection of methods for uncertainty quantification and propagation using Dempster-Shafer Theory and imprecise probabilities.
OpenTURNS | The official OpenTURNS Website
Mathematics | 18.102 Introduction to Functional Analysis, Spring 2009
Polynomial chaos for the approximation of uncertainties: Chances and limits
Comparison of Non-Intrusive Polynomial Chaos and Stochastic Collocation Methods for Uncertainty Quantification Comparison of Non-Intrusive Polynomial Chaos and Stochastic Collocation Methods for Uncertainty Quantification ( Citations: 7 ) Non-intrusive polynomial chaos expansion (PCE) and stochastic collocation (SC) meth- ods are attractive techniques for uncertainty quantification (UQ) due to their strong math- ematical basis and ability to produce functional representations of stochastic variability. PCE estimates coefficients for known orthogonal polynomial basis functions based on a set of response function evaluations, using sampling, linear regression, tensor-product quadra- ture, or Smolyak sparse grid approaches.
Academic Publications Evaluation of Non-Intrusive Approaches for Wiener-Askey Generalized Polynomial Chaos Evaluation of Non-Intrusive Approaches for Wiener-Askey Generalized Polynomial Chaos
Lebesgue integration The integral of a positive function can be interpreted as the area under a curve.
Informally, a measure has the property of being monotone in the sense that if A is a subset of B , the measure of A is less than or equal to the measure of B . Furthermore, the measure of the empty set is required to be 0. Measure (mathematics)
L2-Space On a measure space