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SIAM Journal on Scientific Computing, ISSN 1064-8275, 2006, Volume 27, Issue 3, pp. 1118 - 1139
Recently there has been a growing interest in designing efficient methods for the solution of ordinary/ partial differential equations with random inputs. To... 
Collocation methods | Uncertainty quantification | Stochastic inputs | Differential equations | MONOMIAL CUBATURE RULES | CHAOS | MATHEMATICS, APPLIED | uncertainty quantification | STROUD | STOCHASTIC FINITE-ELEMENTS | MODELING UNCERTAINTY | stochastic inputs | SIMULATIONS | collocation methods | differential equations
Journal Article
SIAM Journal on Scientific Computing, ISSN 1064-8275, 2014, Volume 36, Issue 2, pp. A495 - A521
We present a numerical method for utilizing stochastic models with differing fidelities to approximate parameterized functions. A representative case is where... 
Multifidelity models | Nonintrusive stochastic collocation | Model-order reduction | MATHEMATICS, APPLIED | REDUCED BASIS METHOD | GREEDY ALGORITHMS | PARTIAL-DIFFERENTIAL-EQUATIONS | nonintrusive stochastic collocation | FEKETE | model-order reduction | OPTIMIZATION | POINTS | multifidelity models
Journal Article
International Journal for Numerical Methods in Engineering, ISSN 0029-5981, 03/2020, Volume 121, Issue 6, pp. 1314 - 1343
Journal Article
Computer Methods in Applied Mechanics and Engineering, ISSN 0045-7825, 07/2016, Volume 306, pp. 95 - 122
Journal Article
Communications in Computational Physics, ISSN 1815-2406, 07/2015, Volume 18, Issue 1, pp. 1 - 36
Collocation has become a standard tool for approximation of parameterized systems in the uncertainty quantification (UQ) community. Techniques for... 
least interpolation | least-squares | Stochastic collocation | compressive sampling | unstructured methes | LEBESGUE FUNCTIONS | POLYNOMIAL INTERPOLATION | APPROXIMATIONS | SIGNAL RECOVERY | ALGORITHMS | PHYSICS, MATHEMATICAL | CHAOS | FEKETE POINTS | PARTIAL-DIFFERENTIAL-EQUATIONS | UNCERTAINTY | CONSTRUCTIONS
Journal Article
Applied Mathematics and Computation, ISSN 0096-3003, 11/2014, Volume 247, pp. 1011 - 1020
A numerical method for solving nonlinear Stochastic Itô–Volterra equations is proposed. The method is based on delta function (DF) approximations. The... 
Delta functions | Error analysis | Stochastic | Collocation | Vector forms | Operational matrices | MATHEMATICS, APPLIED | NUMERICAL-SOLUTION | RANDOM DIFFERENTIAL-EQUATIONS | INTEGRODIFFERENTIAL EQUATIONS | Approximation | Computation | Mathematical analysis | Nonlinearity | Mathematical models | Stochasticity | Dynamical systems | Delta function
Journal Article
Mathematics of Computation of the American Mathematical Society, ISSN 0025-5718, 07/2017, Volume 86, Issue 306, pp. 1913 - 1947
We propose, theoretically investigate, and numerically validate an algorithm for the Monte Carlo solution of least-squares polynomial approximation problems in... 
PROJECTION | CHAOS | MATHEMATICS, APPLIED | MARKOV-TYPE | POLYNOMIAL-APPROXIMATION | BERGMAN KERNELS | EQUILIBRIUM MEASURES | ASYMPTOTICS | STOCHASTIC COLLOCATION | MATHEMATICS AND COMPUTING
Journal Article