A
Akil Narayan
Researcher at University of Utah
Publications - 147
Citations - 1856
Akil Narayan is an academic researcher from University of Utah. The author has contributed to research in topics: Polynomial chaos & Uncertainty quantification. The author has an hindex of 20, co-authored 125 publications receiving 1369 citations. Previous affiliations of Akil Narayan include University of Massachusetts Dartmouth & Brown University.
Papers
More filters
Journal ArticleDOI
A stochastic collocation algorithm with multifidelity models
TL;DR: This work presents a numerical method for utilizing stochastic models with differing fideli- ties to approximate parameterized functions, and provides sufficient conditions for convergence, and presents several examples that are of practical interest, including multifidelity approximations and dimensionality reduction.
Journal ArticleDOI
Adaptive Leja Sparse Grid Constructions for Stochastic Collocation and High-Dimensional Approximation
Akil Narayan,John D. Jakeman +1 more
TL;DR: In this article, an adaptive sparse grid stochastic collocation approach based upon Leja interpolation sequences for approximation of parameterized functions with high-dimensional parameters is proposed, where the weights are determined by the probability densities of the random variables.
Journal ArticleDOI
Stochastic collocation methods on unstructured grids in high dimensions via interpolation
Akil Narayan,Dongbin Xiu +1 more
TL;DR: This paper presents the framework of least orthogonal interpolation, which allows one to construct interpolation polynomials based on arbitrarily located grids in arbitrary dimensions, which enables one to conduct stochastic collocation simulations in practical problems where one cannot adopt some popular node selections.
Journal ArticleDOI
A Christoffel function weighted least squares algorithm for collocation approximations
TL;DR: This work proposes an algorithm for the Monte Carlo solution of least-squares polynomial approximation problems in a collocation frame- work, and presents theoretical analysis to motivate the algorithm, and numerical results that show the method is superior to standard Monte Carlo methods in many situations of interest.
Journal ArticleDOI
A Generalized Sampling and Preconditioning Scheme for Sparse Approximation of Polynomial Chaos Expansions
TL;DR: In this article, the authors proposed an algorithm for recovering sparse orthogonal polynomial expansions via collocation, where the weights of the diagonal preconditioning matrix are given by evaluations of the Christoffel function.