102 citations · 787 across the 61 of their papers we have counts for
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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-…
A Reduced Radial Basis Function Method for Partial Differential Equations on irregular domains
Yanlai Chen, Sigal Gottlieb, Alfa Heryudono +1
We propose and test the first Reduced Radial Basis Function Method (RBFM) for solving parametric partial differential equations on irregular domains. The two major ingredients…
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…
Multivariate discrete least-squares approximations with a new type of collocation grid
Tao Zhou, Akil Narayan, Zhiqiang Xu
In this work, we discuss the problem of approximating a multivariate function by discrete least squares projection onto a polynomial space using a specially designed deterministic…