On the Decay Rate of the Singular Values of Bivariate Functions
暂无分享,去创建一个
[1] Vladimir N. Temlyakov,et al. Hyperbolic Cross Approximation , 2016, 1601.03978.
[2] Victor M. Calo,et al. Randomized Oversampling for Generalized Multiscale Finite Element Methods , 2014, Multiscale Model. Simul..
[3] Arieh Iserles,et al. From high oscillation to rapid approximation I: Modified Fourier expansions , 2008 .
[4] S. Yau,et al. On the parabolic kernel of the Schrödinger operator , 1986 .
[5] R. Ghanem,et al. Stochastic Finite Elements: A Spectral Approach , 1990 .
[6] A. Iserles,et al. From high oscillation to rapid approximation II: expansions in Birkhoff series , 2012 .
[7] Christoph Schwab,et al. Karhunen-Loève approximation of random fields by generalized fast multipole methods , 2006, J. Comput. Phys..
[8] Holger Wendland,et al. Approximation by positive definite kernels , 2002 .
[9] Lawrence Sirovich,et al. Empirical and Stokes eigenfunctions and the far‐dissipative turbulent spectrum , 1990 .
[10] Albert Cohen,et al. Approximation of high-dimensional parametric PDEs * , 2015, Acta Numerica.
[11] Claude Jeffrey Gittelson,et al. Sparse tensor discretizations of high-dimensional parametric and stochastic PDEs* , 2011, Acta Numerica.
[12] Reinhold Schneider,et al. Approximation rates for the hierarchical tensor format in periodic Sobolev spaces , 2014, J. Complex..
[13] Hikosaburo Komatsu,et al. Fractional powers of operators. , 1966 .
[14] A. Caponnetto,et al. Optimal Rates for the Regularized Least-Squares Algorithm , 2007, Found. Comput. Math..
[15] F. B. Belgacem,et al. Karhunen–Loève’s truncation error for bivariate functions , 2015 .
[16] Albert Cohen,et al. Fully Discrete Approximation of Parametric and Stochastic Elliptic PDEs , 2017, SIAM J. Numer. Anal..
[17] V. Temlyakov. Estimates of best bilinear approximations of functions and approximation numbers of integral operators , 1992 .
[18] Yalchin Efendiev,et al. Generalized multiscale finite element methods (GMsFEM) , 2013, J. Comput. Phys..
[19] Albert Cohen,et al. Representations of Gaussian Random Fields and Approximation of Elliptic PDEs with Lognormal Coefficients , 2016, Journal of Fourier Analysis and Applications.
[20] Raúl Tempone,et al. Galerkin Finite Element Approximations of Stochastic Elliptic Partial Differential Equations , 2004, SIAM J. Numer. Anal..
[21] Wolfgang Dahmen,et al. Tensor-Sparsity of Solutions to High-Dimensional Elliptic Partial Differential Equations , 2014, Found. Comput. Math..
[22] Ronald DeVore,et al. The Theoretical Foundation of Reduced Basis Methods , 2014 .
[23] A. Pietsch. Eigenvalue distribution of compact operators , 1986 .
[24] Felipe Cucker,et al. On the mathematical foundations of learning , 2001 .
[25] Dr. M. G. Worster. Methods of Mathematical Physics , 1947, Nature.
[26] R. DeVore,et al. Nonlinear approximation , 1998, Acta Numerica.
[27] Hyunjoong Kim,et al. Functional Analysis I , 2017 .
[28] S. Agmon. Lectures on Elliptic Boundary Value Problems , 1965 .
[29] N. Meyers. An $L^p$-estimate for the gradient of solutions of second order elliptic divergence equations , 1963 .
[30] Radu Alexandru Todor,et al. Robust Eigenvalue Computation for Smoothing Operators , 2006, SIAM J. Numer. Anal..
[31] G. Burton. Sobolev Spaces , 2013 .
[32] H. Triebel. Theory of Function Spaces III , 2008 .
[33] Guanglian Li,et al. Multiscale model reduction for high-contrast flow problems , 2015 .
[34] I. Babuska,et al. The partition of unity finite element method: Basic theory and applications , 1996 .
[35] M. B. A. Babaev. Approximation to the Sobolev classesWqr of functions of several variables by bilinear forms inLp for 2≤q≤p≤∞ , 1997 .
[36] Albert Cohen,et al. Convergence Rates of Best N-term Galerkin Approximations for a Class of Elliptic sPDEs , 2010, Found. Comput. Math..
[37] A. V. Balakrishnan,et al. Fractional powers of closed operators and the semigroups generated by them. , 1960 .
[38] A. Pietsch. Eigenvalues and S-Numbers , 1987 .
[39] Michael Griebel,et al. Approximation of bi-variate functions: singular value decomposition versus sparse grids , 2014 .