Journal of Algorithms
Matrix computations (3rd ed.)
Iterative methods for solving linear systems
Iterative methods for solving linear systems
A Multilinear Singular Value Decomposition
SIAM Journal on Matrix Analysis and Applications
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
Efficient MATLAB Computations with Sparse and Factored Tensors
SIAM Journal on Scientific Computing
Tensor Rank and the Ill-Posedness of the Best Low-Rank Approximation Problem
SIAM Journal on Matrix Analysis and Applications
Tucker Dimensionality Reduction of Three-Dimensional Arrays in Linear Time
SIAM Journal on Matrix Analysis and Applications
Tensor decomposition in electronic structure calculations on 3D Cartesian grids
Journal of Computational Physics
Linear algebra for tensor problems
Computing
SIAM Journal on Matrix Analysis and Applications
Multigrid Accelerated Tensor Approximation of Function Related Multidimensional Arrays
SIAM Journal on Scientific Computing
Tensor Decompositions and Applications
SIAM Review
Breaking the Curse of Dimensionality, Or How to Use SVD in Many Dimensions
SIAM Journal on Scientific Computing
Approximation of $2^d\times2^d$ Matrices Using Tensor Decomposition
SIAM Journal on Matrix Analysis and Applications
Numerical Solution of the Hartree-Fock Equation in Multilevel Tensor-Structured Format
SIAM Journal on Scientific Computing
SIAM Journal on Scientific Computing
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New algorithms are proposed for the Tucker approximation of a 3-tensor accessed only through a tensor-by-vector-by-vector multiplication subroutine. In the matrix case, the Krylov methods are methods of choice to approximate the dominant column and row subspaces of a sparse or structured matrix given through a matrix-by-vector operation. Using the Wedderburn rank reduction formula, we propose a matrix approximation algorithm that computes the Krylov subspaces and can be generalized to 3-tensors. The numerical experiments show that on quantum chemistry data the proposed tensor methods outperform the minimal Krylov recursion of Savas and Eldén.