A tensor bidiagonalization method for higher‐order singular value decomposition with applications
Copyright policy )A tensor bidiagonalization method for higher‐order singular value decomposition with applications
AbstractThe need to know a few singular triplets associated with the largest singular values of a third‐order tensor arises in data compression and extraction. This paper describes a new method for their computation using the t‐product. Methods for determining a couple of singular triplets associated with the smallest singular values also are presented. The proposed methods generalize available restarted Lanczos bidiagonalization methods for computing a few of the largest or smallest singular triplets of a matrix. The methods of this paper use Ritz and harmonic Ritz lateral slices to determine accurate approximations of the largest and smallest singular triplets, respectively. Computed examples show applications to data compression and face recognition.
- University System of Ohio United States
- University of the Littoral Opal Coast France
- Laboratoire de Mathématiques France
- Kent State University United States
- Université Mohammed VI Polytechnique Morocco
Composite material, Tensor Decompositions and Applications in Multilinear Algebra, Higher-Order Tensors, Tensor (intrinsic definition), Matrix (chemical analysis), Singular Value Decomposition, restarted tensor bidiagonalization, Mathematical analysis, Quantum mechanics, Factorization of matrices, Artificial Intelligence, Multilinear algebra, tensor calculus, FOS: Mathematics, Mathematics - Numerical Analysis, Singular solution, Singular spectrum analysis, Matrix Algorithms and Iterative Methods, Eigenvalues and eigenvectors, Text Compression and Indexing Algorithms, Physics, Lanczos resampling, singular value decomposition, Singular value decomposition, Pure mathematics, partial tensor bidiagonalization, Numerical Analysis (math.NA), Applied mathematics, tensor, Materials science, Algorithm, Computational Mathematics, Singular value, Tensor product, Computational Theory and Mathematics, t-product, Physical Sciences, Computer Science, Tensor Decomposition, Computation, Mathematics, face recognition, Matrix Computations
Composite material, Tensor Decompositions and Applications in Multilinear Algebra, Higher-Order Tensors, Tensor (intrinsic definition), Matrix (chemical analysis), Singular Value Decomposition, restarted tensor bidiagonalization, Mathematical analysis, Quantum mechanics, Factorization of matrices, Artificial Intelligence, Multilinear algebra, tensor calculus, FOS: Mathematics, Mathematics - Numerical Analysis, Singular solution, Singular spectrum analysis, Matrix Algorithms and Iterative Methods, Eigenvalues and eigenvectors, Text Compression and Indexing Algorithms, Physics, Lanczos resampling, singular value decomposition, Singular value decomposition, Pure mathematics, partial tensor bidiagonalization, Numerical Analysis (math.NA), Applied mathematics, tensor, Materials science, Algorithm, Computational Mathematics, Singular value, Tensor product, Computational Theory and Mathematics, t-product, Physical Sciences, Computer Science, Tensor Decomposition, Computation, Mathematics, face recognition, Matrix Computations
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