Fast Multidimensional Convolution in Low-Rank Tensor Formats via Cross Approximation
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Publication:5254416
DOI10.1137/140958529zbMath1320.65197arXiv1402.5649OpenAlexW1995838359MaRDI QIDQ5254416
Ivan V. Oseledets, M. V. Rakhuba
Publication date: 9 June 2015
Published in: SIAM Journal on Scientific Computing (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/1402.5649
multilinear algebracross approximationtensor decompositionsmultidimensional convolutiontensor trainblack box approximation
Convolution as an integral transform (44A35) Numerical methods for discrete and fast Fourier transforms (65T50) Numerical methods for integral transforms (65R10) Multilinear algebra, tensor calculus (15A69)
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Uses Software
Cites Work
- Unnamed Item
- Unnamed Item
- Tensor Decompositions and Applications
- Tensor-Train Decomposition
- TT-cross approximation for multidimensional arrays
- The density-matrix renormalization group in the age of matrix product states
- Adaptive cross approximation of multivariate functions
- \(O(d \log N)\)-quantics approximation of \(N\)-\(d\) tensors in high-dimensional numerical modeling
- Low-rank Kronecker-product approximation to multi-dimensional nonlocal operators I. Separable approximation of multi-variate functions
- Low-rank Kronecker-product approximation to multi-dimensional nonlocal operators II. HKT representation of certain operators
- Tensor decomposition in electronic structure calculations on 3D Cartesian grids
- Linear algebra for tensor problems
- An introduction to mathematical models of coagulation--fragmentation processes: a discrete deterministic mean-field approach
- On cross approximation of multi-index arrays
- Efficient convolution with the Newton potential in \(d\) dimensions
- Generalizing the column-row matrix decomposition to multi-way arrays
- Fast and accurate tensor approximation of a multivariate convolution with linear scaling in dimension
- Incomplete cross approximation in the mosaic-skeleton method
- Approximation of boundary element matrices
- Superfast Fourier transform using QTT approximation
- Black box approximation of tensors in hierarchical Tucker format
- Quasioptimality of maximum-volume cross interpolation of tensors
- A new scheme for the tensor representation
- Computation of the Hartree-Fock exchange by the tensor-structured methods
- An introduction to hierarchical (\(\mathcal H\)-) rank and TT-rank of tensors with examples
- QTT representation of the Hartree and exchange operators in electronic structure calculations
- DMRG approach to fast linear algebra in the TT-format
- Low rank Tucker-type tensor approximation to classical potentials
- Fast and exact projected convolution for non-equidistant grids
- Multilevel Toeplitz Matrices Generated by Tensor-Structured Vectors and Convolution with Logarithmic Complexity
- A literature survey of low-rank tensor approximation techniques
- Sublinear Randomized Algorithms for Skeleton Decompositions
- Wedderburn Rank Reduction and Krylov Subspace Method for Tensor Approximation. Part 1: Tucker Case
- Alternating Minimal Energy Methods for Linear Systems in Higher Dimensions
- Approximate multiplication of tensor matrices based on the individual filtering of factors
- Hierarchical Singular Value Decomposition of Tensors
- Approximation of $2^d\times2^d$ Matrices Using Tensor Decomposition
- Numerical Solution of the Hartree–Fock Equation in Multilevel Tensor-Structured Format
- Efficient Options Pricing Using the Fast Fourier Transform
- Tensor Spaces and Numerical Tensor Calculus
- Breaking the Curse of Dimensionality, Or How to Use SVD in Many Dimensions
- Multigrid Accelerated Tensor Approximation of Function Related Multidimensional Arrays
- Optimal and Superoptimal Circulant Preconditioners
- A Multilinear Singular Value Decomposition
- On the Best Rank-1 and Rank-(R1 ,R2 ,. . .,RN) Approximation of Higher-Order Tensors
- Numerical operator calculus in higher dimensions
- Fast truncation of mode ranks for bilinear tensor operations
- Tensor-Structured Factorized Calculation of Two-Electron Integrals in a General Basis
- Tucker Dimensionality Reduction of Three-Dimensional Arrays in Linear Time
- Tensor Rank and the Ill-Posedness of the Best Low-Rank Approximation Problem
- Black-Box Hartree–Fock Solver by Tensor Numerical Methods
- Structured Rank-(r1, . . . , rd) Decomposition of Function-related Tensors in R_D
- Algorithms for Numerical Analysis in High Dimensions
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