Numerical Computation for Orthogonal Low-Rank Approximation of Tensors
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Publication:5237898
DOI10.1137/18M1208101zbMath1435.65064OpenAlexW2972630054WikidataQ114074292 ScholiaQ114074292MaRDI QIDQ5237898
Publication date: 25 October 2019
Published in: SIAM Journal on Matrix Analysis and Applications (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1137/18m1208101
Numerical solutions to overdetermined systems, pseudoinverses (65F20) Numerical solutions to equations with linear operators (65J10) Approximation algorithms (68W25) Multilinear algebra, tensor calculus (15A69) Orthogonalization in numerical linear algebra (65F25) Numerical methods for low-rank matrix approximation; matrix compression (65F55)
Related Items (15)
Hermitian and skew-Hermitian splitting methods for solving a tensor equation ⋮ -SKEW-HERMITIAN SOLUTION TO A SYSTEM OF TENSOR EQUATIONS OVER THE QUATERNION ALGEBRA ⋮ On RGI algorithms for solving Sylvester tensor equations ⋮ On approximation algorithm for orthogonal low-rank tensor approximation ⋮ FINDING ITERATIVE ALGORITHMS FOR SOLVING GENERALIZED COUPLED SYLVESTER TENSOR EQUATIONS ⋮ The least-squares solution with the least norm to a system of tensor equations over the quaternion algebra ⋮ A system of coupled two-sided Sylvester-type tensor equations over the quaternion algebra ⋮ The accelerated overrelaxation splitting method for solving symmetric tensor equations ⋮ Linear convergence of an alternating polar decomposition method for low rank orthogonal tensor approximations ⋮ Half-quadratic alternating direction method of multipliers for robust orthogonal tensor approximation ⋮ Rank properties and computational methods for orthogonal tensor decompositions ⋮ Structure Preserving Quaternion Biconjugate Gradient Method ⋮ The Epsilon-Alternating Least Squares for Orthogonal Low-Rank Tensor Approximation and Its Global Convergence ⋮ Developing iterative algorithms to solve Sylvester tensor equations ⋮ Reducible solution to a quaternion tensor equation
Uses Software
Cites Work
- Tensor Decompositions and Applications
- Tensor numerical methods in scientific computing
- On the non-existence of optimal solutions and the occurrence of ``degeneracy in the CANDECOMP/PARAFAC model
- Tensor-based techniques for the blind separation of DS-CDMA signals
- Greedy algorithms and \(M\)-term approximation with regard to redundant dictionaries
- A singular value decomposition of a \(k\)-way array for a principal component analysis of multiway data, \(\text{PTA-}k\)
- The ubiquitous Kronecker product
- Convergence analysis of an SVD-based algorithm for the best rank-1 tensor approximation
- Monotonically convergent algorithms for symmetric tensor approximation
- Degeneracy in Candecomp/Parafac explained for \(p\times p\times 2\) arrays of rank \(p+1\) or higher
- Positive definiteness and semi-definiteness of even order symmetric Cauchy tensors
- Circulant tensors with applications to spectral hypergraph theory and stochastic process
- Infinite and finite dimensional Hilbert tensors
- Tensor-product approximation to operators and functions in high dimensions
- Analysis of individual differences in multidimensional scaling via an \(n\)-way generalization of ``Eckart-Young decomposition
- Orthogonal Tensor Decompositions
- Rank-One Approximation to High Order Tensors
- On the Global Convergence of the Alternating Least Squares Method for Rank-One Approximation to Generic Tensors
- On best rank one approximation of tensors
- SVD-Based Algorithms for the Best Rank-1 Approximation of a Symmetric Tensor
- Computing a Trust Region Step
- Orthogonal Low Rank Tensor Approximation: Alternating Least Squares Method and Its Global Convergence
- Multigrid Accelerated Tensor Approximation of Function Related Multidimensional Arrays
- On the Tensor SVD and the Optimal Low Rank Orthogonal Approximation of Tensors
- Computing the Polar Decomposition—with Applications
- A Multilinear Singular Value Decomposition
- On the Best Rank-1 and Rank-(R1 ,R2 ,. . .,RN) Approximation of Higher-Order Tensors
- Blind Identification of Underdetermined Mixtures by Simultaneous Matrix Diagonalization
- The uniqueness of multilinear PageRank vectors
- Probabilistic Tensor Canonical Polyadic Decomposition With Orthogonal Factors
- Canonical Polyadic Decomposition with a Columnwise Orthonormal Factor Matrix
- The Numerical Solution of Systems of Polynomials Arising in Engineering and Science
- Low-Rank Approximation of Generic $p \timesq \times2$ Arrays and Diverging Components in the Candecomp/Parafac Model
- Tensor Rank and the Ill-Posedness of the Best Low-Rank Approximation Problem
- Khatri-Rao space-time codes
- Hierarchical Kronecker tensor-product approximations
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