Polynomial Spectral Methods
We examine the use of global polynomial approximations of model outputs as a function of inputs.
Documents
| Homework2.pdf | Homework 2. |
| quad_script.m | Script for getting started with the quadrature rules in PMPack. |
| pmpack.tgz | A suite of Matlab tools for working orthogonal polynomials and quadrature. |
| outline11.pdf | Handout for lecture 11. |
| outline12.pdf | Handout for lecture 12. |
| outline13.pdf | Handout for lecture 13. |
References
- Spectral Methods for Parameterized Matrix Equations. Paul Constantine, David Gleich, and Gianluca Iaccarino.
- High-Order Collocation Methods for Differential Equations with Random Inputs. Dongbin Xiu and Jan S. Hesthaven.
- The Wiener--Askey Polynomial Chaos for Stochastic Differential Equations. Dongbin Xiu and George Em Karniadakis.
- Is Gauss Quadrature Better than Clenshaw-Curtis? Lloyd N. Trefethen.