A Lanczos-Stieltjes method for one-dimensional ridge function approximation and integration
Autor: | Glaws, Andrew, Constantine, Paul G. |
---|---|
Rok vydání: | 2018 |
Předmět: | |
Druh dokumentu: | Working Paper |
Popis: | 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. Comment: 24 pages, 14 figures |
Databáze: | arXiv |
Externí odkaz: |