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MATHICSE Technical Report : Discrete least-squares approximations over optimized downward closed polynomial spaces in arbitrary dimension

Fabio Nobile, Giovanni Migliorati

We analyze the accuracy of the discrete least-squares approximation of a function u in multivariate polynomial spaces

P_\Lambda := span\{y \mapsto y^\nu | \nu \in \Lambda\}

with

\Lambda\subset N_0^d

over the domain

\Gamma := [-1,1]^d

, based on the sa ...

MATHICSE2015

Fabio Nobile

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MATHICSE Technical Report : Discrete least-squares approximations over optimized downward closed polynomial spaces in arbitrary dimension

Convergence estimates in probability and in expectation for discrete least squares with noisy evaluations at random points

MATHICSE Technical Report : Convergence estimates in probability and in expectation for discrete least squares with noisy evaluations at random points

MATHICSE Technical Report : Multi-index stochastic collocation convergence rates for random PDEs with parametric regularity

Analysis of discrete least squares on multivariate polynomial spaces with evaluations at low-discrepancy point sets

MATHICSE Technical Report : Analysis of discrete least squares on multivariate polynomial spaces with evaluations at low-discrepancy point sets

MATHICSE Technical Report : Multi-index stochastic collocation for random PDEs

Analysis and computation of the elastic wave equation with random coefficients

Comparison of Clenshaw-Curtis and Leja Quasi-Optimal Sparse Grids for the Approximation of Random PDEs

An effective algorithm for the generation of patient-specific Purkinje networks in computational electrocardiology

MATHICSE Technical Report : Multi-index stochastic collocation for random PDEs

MATHICSE Technical Report : Multi-index stochastic collocation convergence rates for random PDEs with parametric regularity

MATHICSE Technical Report : Discrete least-squares approximations over optimized downward closed polynomial spaces in arbitrary dimension

Convergence estimates in probability and in expectation for discrete least squares with noisy evaluations at random points

MATHICSE Technical Report : Convergence estimates in probability and in expectation for discrete least squares with noisy evaluations at random points

Comparison of Clenshaw-Curtis and Leja Quasi-Optimal Sparse Grids for the Approximation of Random PDEs

Analysis of discrete least squares on multivariate polynomial spaces with evaluations at low-discrepancy point sets

An effective algorithm for the generation of patient-specific Purkinje networks in computational electrocardiology

Analysis and computation of the elastic wave equation with random coefficients

MATHICSE Technical Report : Analysis of discrete least squares on multivariate polynomial spaces with evaluations at low-discrepancy point sets