9 citations · 14 across the 6 of their papers we have counts for
7 papers
Nonlinear approximation of high-dimensional anisotropic analytic functions
Diane Guignard, Peter Jantsch
Motivated by nonlinear approximation results for classes of parametric partial differential equations (PDEs), we seek to better understand so-called library approximations to analy…
Nonlinear Methods for Model Reduction
Andrea Bonito, Albert Cohen, Ronald DeVore +3
The usual approach to model reduction for parametric partial differential equations (PDEs) is to construct a linear space which approximates well the solution manifold $\math…
Polynomial Approximation of Anisotropic Analytic Functions of Several Variables
Andrea Bonito, Ronald DeVore, Diane Guignard +2
Motivated by numerical methods for solving parametric partial differential equations, this paper studies the approximation of multivariate analytic functions by algebraic polynomia…
On the Lebesgue Constant of Weighted Leja Points for Lagrange Interpolation on Unbounded Domains
Peter Jantsch, Clayton G. Webster, Guannan Zhang
This work focuses on weighted Lagrange interpolation on an unbounded domain, and analyzes the Lebesgue constant for a sequence of weighted Leja points. The standard Leja points are…
Rectified Simplex Polytope Numbers
Michael A. Jackson, Doug Smith, Peter Jantsch +5
Polytope numbers for a given polytope are an integer sequence defined by the combinatorics of the polytope. Recent work by H. K. Kim and J. Y. Lee has focused on writing polytope n…
Accelerating stochastic collocation methods for partial differential equations with random input data
Diego Galindo, Peter Jantsch, Clayton G. Webster +1
This work proposes and analyzes a generalized acceleration technique for decreasing the computational complexity of using stochastic collocation (SC) methods to solve partial diffe…