Uncertainty quantification under dependent random variables by a generalized polynomial dimensional decomposition

DOI10.1016/j.cma.2018.09.026zbMath1440.60044OpenAlexW2898442686WikidataQ129076818 ScholiaQ129076818MaRDI QIDQ1986743

Sharif Rahman

Publication date: 9 April 2020

Published in: Computer Methods in Applied Mechanics and Engineering (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.cma.2018.09.026

zbMATH Keywords

ANOVAmultivariate orthogonal polynomialsnon-product-type probability measures

Mathematics Subject Classification ID

Computational methods for problems pertaining to probability theory (60-08) Stochastic processes (60G99) Analysis of variance and covariance (ANOVA) (62J10)

Related Items (3)

Practical uncertainty quantification analysis involving statistically dependent random variables ⋮ A novel algorithm for the stochastic analysis of electric field problems considering material and spatial uncertainties ⋮ Dimensionwise multivariate orthogonal polynomials in general probability spaces

Cites Work

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• Adaptive-sparse polynomial dimensional decomposition methods for high-dimensional stochastic computing
• Dimension-wise integration of high-dimensional functions with applications to finance
• Numerical integration using sparse grids
• General foundations of high-dimensional model representations
• The \(d\)-variate vector Hermite polynomial of order \(k\)
• Adaptive surrogate modeling by ANOVA and sparse polynomial dimensional decomposition for global sensitivity analysis in fluid simulation
• Sparse grid collocation schemes for stochastic natural convection problems
• Orthogonal polynomials in two variables
• Wiener-Hermite polynomial expansion for multivariate Gaussian probability measures
• The orthogonal development of non-linear functionals in series of Fourier-Hermite functionals
• A Generalized ANOVA Dimensional Decomposition for Dependent Probability Measures
• ORTHOGONAL POLYNOMIAL EXPANSIONS FOR SOLVING RANDOM EIGENVALUE PROBLEMS
• Mathematical Properties of Polynomial Dimensional Decomposition
• Approximation errors in truncated dimensional decompositions
• A polynomial dimensional decomposition for stochastic computing
• Lanczos Algorithms for Large Symmetric Eigenvalue Computations
• A generalized dimension‐reduction method for multidimensional integration in stochastic mechanics
• A Class of Statistics with Asymptotically Normal Distribution
• A Stochastic Collocation Method for Elliptic Partial Differential Equations with Random Input Data

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