Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A generalized sampling and preconditioning scheme for sparse
  approximation of polynomial chaos expansions   In this paper we propose an algorithm for recovering sparse orthogonal
polynomials using stochastic collocation. Our approach is motivated by the
desire to use generalized polynomial chaos expansions (PCE) to quantify
uncertainty in models subject to uncertain input parameters. The standard
sampling approach for recovering sparse polynomials is to use Monte Carlo (MC)
sampling of the density of orthogonality. However MC methods result in poor
function recovery when the polynomial degree is high. Here we propose a general
algorithm that can be applied to any admissible weight function on a bounded
domain and a wide class of exponential weight functions defined on unbounded
domains. Our proposed algorithm samples with respect to the weighted
equilibrium measure of the parametric domain, and subsequently solves a
preconditioned $\ell^1$-minimization problem, where the weights of the diagonal
preconditioning matrix are given by evaluations of the Christoffel function. We
present theoretical analysis to motivate the algorithm, and numerical results
that show our method is superior to standard Monte Carlo methods in many
situations of interest. Numerical examples are also provided that demonstrate
that our proposed Christoffel Sparse Approximation algorithm leads to
comparable or improved accuracy even when compared with Legendre and Hermite
specific algorithms.

4
The categories of this paper are: cond-mat
10
The categories of this paper are: q-bio
3
The categories of this paper are: physics
8
The categories of this paper are: hep-ex
28
The categories of this paper are: alg-geom
14
The categories of this paper are: math-ph
27
The categories of this paper are: comp-gas
34
The categories of this paper are: chem-ph
20
The categories of this paper are: acc-phys
22
The categories of this paper are: chao-dyn
29
The categories of this paper are: funct-an
23
The categories of this paper are: solv-int
32
The categories of this paper are: atom-ph
7
The categories of this paper are: hep-th
19
The categories of this paper are: eess
12
The categories of this paper are: nucl-th