Name
Title | ||
|---|---|---|
Weighted discrete least-squares polynomial approximation using randomized quadratures |
Abstract | ||
|---|---|---|
We discuss the problem of polynomial approximation of multivariate functions using discrete least squares collocation. The problem stems from uncertainty quantification (UQ), where the independent variables of the functions are random variables with specified probability measure. We propose to construct the least squares approximation on points randomly and uniformly sampled from tensor product Gaussian quadrature points. We analyze the stability properties of this method and prove that the method is asymptotically stable, provided that the number of points scales linearly (up to a logarithmic factor) with the cardinality of the polynomial space. Specific results in both bounded and unbounded domains are obtained, along with a convergence result for Chebyshev measure. Numerical examples are provided to verify the theoretical results. |
Year | DOI | Venue |
|---|---|---|
2015 | 10.1016/j.jcp.2015.06.042 | Journal of Computational Physics |
Keywords | Field | DocType |
Least squares method,Orthogonal polynomials,Generalized polynomial chaos,Uncertainty quantification | Least squares,Tensor product,Stable polynomial,Mathematical optimization,Random variable,Polynomial,Mathematical analysis,Probability measure,Matrix polynomial,Gaussian quadrature,Mathematics | Journal |
Volume | Issue | ISSN |
298 | C | 0021-9991 |
Citations | PageRank | References |
3 | 0.39 | 21 |
Authors | ||
3 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Tao ZHOU | 1 | 85 | 15.92 |
| Akil Narayan | 2 | 77 | 12.59 |
| Dongbin Xiu | 3 | 1068 | 115.57 |