Greedy algorithms and M-term approximation with regard to redundant dictionaries
Journal of Approximation Theory
On the Best Rank-1 and Rank-(R1,R2,. . .,RN) Approximation of Higher-Order Tensors
SIAM Journal on Matrix Analysis and Applications
Rank-One Approximation to High Order Tensors
SIAM Journal on Matrix Analysis and Applications
Orthogonal Tensor Decompositions
SIAM Journal on Matrix Analysis and Applications
SIAM Journal on Matrix Analysis and Applications
Algorithms for Numerical Analysis in High Dimensions
SIAM Journal on Scientific Computing
Tensor decomposition in electronic structure calculations on 3D Cartesian grids
Journal of Computational Physics
Dynamical Tensor Approximation
SIAM Journal on Matrix Analysis and Applications
Approximation of the electron density of Aluminium clusters in tensor-product format
Journal of Computational Physics
A New Truncation Strategy for the Higher-Order Singular Value Decomposition
SIAM Journal on Scientific Computing
An equi-directional generalization of adaptive cross approximation for higher-order tensors
Applied Numerical Mathematics
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In recent papers tensor-product structured Nystrom and Galerkin-type approximations of certain multi-dimensional integral operators have been introduced and analysed. In the present paper, we focus on the analysis of the collocation-type schemes with respect to the tensor-product basis in a high spatial dimension d. Approximations up to an accuracy O(N^-^@a^/^d) are proven to have the storage complexity O(dN^1^/^dlog^qN) with q independent of d, where N is the discrete problem size. In particular, we apply the theory to a collocation discretisation of the Newton potential with the kernel 1|x-y|, x,y@?R^d, d=3. Numerical illustrations are given in the case of d=3.