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• W2982477060 abstract "Many of the input-parameter-to-output-quantity-of-interest maps that arise in computational science admit a surprising low-dimensional structure, where the outputs vary primarily along a handful of directions in the high-dimensional input space. This type of structure is well modeled by a ridge function, which is a composition of a low-dimensional linear transformation with a nonlinear function. If the goal is to compute statistics of the output---e.g., as in uncertainty quantification or robust design---then one should exploit this low-dimensional structure, when present, to accelerate computations. We develop Gaussian quadrature and the associated polynomial approximation for one-dimensional ridge functions. The key elements of our method are (i) approximating the univariate density of the given linear combination of inputs by repeated convolutions and (ii) a Lanczos--Stieltjes method for constructing orthogonal polynomials and Gaussian quadrature." @default.
• W2982477060 created "2019-11-08" @default.
• W2982477060 creator A5072780873 @default.
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• W2982477060 date "2019-01-01" @default.
• W2982477060 modified "2023-09-25" @default.
• W2982477060 title "Gaussian Quadrature and Polynomial Approximation for One-Dimensional Ridge Functions" @default.
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• W2982477060 doi "https://doi.org/10.1137/18m1194894" @default.
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