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Motivated by numerical methods for solving parametric partial differential equations, this paper studies the approximation of multivariate analytic functions by algebraic polynomials.
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A. Bonito, R. DeVore and R. Nochetto. Adaptive finite element methods for elliptic problems with discontinuous coefficients. SIAM Journal on Numerical Analysis, 51(6):3106–3134, 2013
A. Chkifa, A. Cohen, C. Schwab. Breaking the curse of dimensionality in sparse polynomial approximation of parametric PDEs. Journal Math. Pures Appl. 9(2) 400–428, 2015
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A. Cohen and R. DeVore. Approximation of high-dimensional parametric PDEs. Acta Numerica, 24:1–159, 2015
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M. Griebel, J. Oettershagen. On tensor product approximation of analytic functions, J. Approx. Theory, 207, 348–379, 2016
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M. Bachmayr, A. Cohen and G. Migliorati. Sparse polynomial approximation of parametric elliptic PDEs. Part I: affine coefficients. ESAIM: Mathematical Modelling and Numerical Analysis, 51(1):321–339, 2017
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H. Tran, C. Webster and G. Zhang. Analysis of quasi-optimal polynomial approximations for parameterized PDEs with deterministic and stochastic coefficients. Numerische Mathematik, 137(2):451–493, 2017
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2013
Cited alongside, same era.
A. Chkifa, A. Cohen, R. DeVore and C. Schwab. Sparse adaptive Taylor approximation algorithms for parametric and stochastic elliptic PDEs. ESAIM: Mathematical Modelling and Numerical Analysis, 47(1):253–280, 2013
2013
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J. Beck, F. Nobile, L. Tamellini and R. Tempone. Convergence of quasi-optimal Stochastic Galerkin methods for a class of PDES with random coefficients. Computers and Mathematics with Applications, 67(4):732–751, 2014
2014
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2017
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A. Cohen and G. Migliorati. Multivariate Approximation in Downward Closed Polynomial Spaces. In: Contemporary Computational Mathematics—a Celebration of the 80th Birthday of Ian Sloan. Vols. 1 and 2, Springer, Cham, 233–282, 2018
2018
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J. Zech. Sparse-Grid Approximation of High-Dimensional Parametric PDEs. PhD Thesis 25683: ETH Zürich, 2018, https://doi.org/10.3929/ethz-b-000340651
2018
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