26 citations · 46 across the 28 of their papers we have counts for
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math.NA2015★ 3 cited
Linear collective collocation and Galerkin approximations for parametric and stochastic elliptic PDEs
Dinh Dũng
Consider the parametric elliptic problem \begin{equation} - \operatorname{dv} \big(a(y)(x)\nabla u(y)(x)\big) \ = \ f(x) \quad x \in D, \ y \in [-1,1]^\infty, \quad u|_{\partial D}…
math.NA2015★ 3 cited
High-dimensional periodic sampling on Smolyak grids based on B-spline quasi-interpolation
Dinh Dũng
We constructed linear algorithms of sampling recovery and cubature formulas on Smolyak grids parametrized by of periodic -variate functions having Lipschitz-H…
math.NA2015★ 1 cited
Hyperbolic cross approximation in infinite dimensions
Dinh Dũng, Michael Griebel
We give tight upper and lower bounds of the cardinality of the index sets of certain hyperbolic crosses which reflect mixed Sobolev-Korobov-type smoothness and mixed Sobolev-analyt…