F ¨ Ur Mathematik in Den Naturwissenschaften Leipzig Multigrid Accelerated Tensor Approximation of Function Related Multi-dimensional Arrays Multigrid Accelerated Tensor Approximation of Function…

By Boris N. Khoromskij, Venera Khoromskaia

Subfields: Numerical Methods & Scientific Computing

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Citations in the corpus

A literature survey of low‐rank tensor approximation techniques (2013, neutral): “, based on Hartree-Fock or DFT models [23, 25, 32, 45, 46, 48, 88, 142–147, 151, 157–160];”
Fast Solution of Parabolic Problems in the Tensor Train/Quantized Tensor Train Format with Initial Application to the Fokker-Planck Equation (2012, methodology): “, the multilevel solver for the Hartree–Fock equation in the Tucker format with the canonical representation of the core [27, 26].”
Tensor-Train Decomposition (2011, background): “It is suitable for “small” dimensions, especially for the three-dimensional case [22, 30, 23].”
Superfast Fourier Transform Using QTT Approximation (2012, methodology): “In this way, fast tensor-product convolution with the Newton kernel based on the canonical or/and Tucker tensor decompositions has been developed in [30, 33, 50] and applied to the fully discrete grid-based solution of the Hartree-Fock equation in [26, 35].”
Quasi-Newton Methods on Grassmannians and Multilinear Approximations of Tensors (2009, background): “There is a different line of algorithms for related tensor approximation problems based on ALS and mutltigrid accelerated ALS [34, 35].”
Fast truncation of mode ranks for bilinear tensor operations (2010, methodology): “This problem was approached in [3] using Tucker-ALS algorithm, in [21] by Tucker-ALS with initial guess obtained from the coarser grids, in [12] by Cross3D algorithm, in [24] by individual cross approximation of canonical factors, in [27] by cross approximation of Gram matrices of unfoldings and in ”
Wedderburn Rank Reduction and Krylov Subspace Method for Tensor Approximation. Part 1: Tucker Case (2010, methodology): “Such recompression was done in [4] using the Tucker-ALS algorithm [22, 7], in [20] by the Tucker-ALS with the initial guess obtained from the coarser grids, in [11] by the Cross3D algorithm [25], in [26] by the individual cross approximation of canonical factors and in [32] by the cross approximatio”
Verification of the cross 3D algorithm on quantum chemistry data (2008, methodology): “A detailed discussion of the two-level tensor representations (formats) can be found in [16, 18, 19 ].”
Two-level Tucker-TT-QTT format for optimized tensor calculus (2012, methodology): “As the combined approach, the Tucker-Canonical format was applied to the solution of Hartree-Fock equation [35, 36].”
Constructive Representation of Functions in Low-Rank Tensor Formats (2012, background): “Low-parametric approximation of multivariate functions is very important in high-dimensional applications (ﬁnancial mathematics [33, 36], quantum chemistry [18, 19, 22], multiparametric and stochastic problems [3], and numerical analysis and sci-entiﬁc computing [10, 20, 23]).”
Tensor-product approach to global time-space-parametric discretization of chemical master equation (2012, methodology): “the multilevel solver for the Hartree-Fock equation in the Tucker format with the canonical representation of the core [41, 42].”
Tensor-Structured Preconditioners and Approximate Inverse of Elliptic Operators in ℝd (2009, methodology): “Example 1. Figure 3.2 represents the convergence history for the best orthogonal Tucker [ 24 ] vs. canonical [2] approximations of the Newton/Yukawa potentials on n × n × n grid for n = 2048.”