180 citations · 1.1k across the 26 of their papers we have counts for
4 papers · 1 filter
A Christoffel function weighted least squares algorithm for collocation approximations
Akil Narayan, John D. Jakeman, Tao Zhou
We propose, theoretically investigate, and numerically validate an algorithm for the Monte Carlo solution of least-squares polynomial approximation problems in a collocation frame-…
Enhancing -minimization estimates of polynomial chaos expansions using basis selection
John D. Jakeman, Michael S. Eldred, Khachik Sargsyan
In this paper we present a basis selection method that can be used with -minimization to adaptively determine the large coefficients of polynomial chaos expansions (PCE). T…
Enhancing adaptive sparse grid approximations and improving refinement strategies using adjoint-based a posteriori error estimates
John D. Jakeman, Timothy Wildey
In this paper we present an algorithm for adaptive sparse grid approximations of quantities of interest computed from discretized partial differential equations. We use adjoint-bas…
Adaptive Leja sparse grid constructions for stochastic collocation and high-dimensional approximation
Akil Narayan, John Jakeman
We propose an adaptive sparse grid stochastic collocation approach based upon Leja interpolation sequences for approximation of parameterized functions with high-dimensional parame…