
Randomized Quaternion Singular Value Decomposition for LowRank Approximation
Quaternion matrix approximation problems construct the approximated matr...
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Faster Tensor Train Decomposition for Sparse Data
In recent years, the application of tensors has become more widespread i...
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Performance of the lowrank tensortrain SVD (TTSVD) for large dense tensors on modern multicore CPUs
There are several factorizations of multidimensional tensors into lower...
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Batched computation of the singular value decompositions of order two by the AVX512 vectorization
In this paper a vectorized algorithm for simultaneously computing up to ...
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Singular Value Decomposition in Sobolev Spaces: Part II
Under certain conditions, an element of a tensor product space can be id...
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A New High Performance and Scalable SVD algorithm on Distributed Memory Systems
This paper introduces a high performance implementation of ZoloSVD algo...
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LazySVD: Even Faster SVD Decomposition Yet Without Agonizing Pain
We study kSVD that is to obtain the first k singular vectors of a matri...
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Computing lowrank approximations of largescale matrices with the Tensor Network randomized SVD
We propose a new algorithm for the computation of a singular value decomposition (SVD) lowrank approximation of a matrix in the Matrix Product Operator (MPO) format, also called the Tensor Train Matrix format. Our tensor network randomized SVD (TNrSVD) algorithm is an MPO implementation of the randomized SVD algorithm that is able to compute dominant singular values and their corresponding singular vectors. In contrast to the stateoftheart tensorbased alternating least squares SVD (ALSSVD) and modified alternating least squares SVD (MALSSVD) matrix approximation methods, TNrSVD can be up to 17 times faster while achieving the same accuracy. In addition, our TNrSVD algorithm also produces accurate approximations in particular cases where both ALSSVD and MALSSVD fail to converge. We also propose a new algorithm for the fast conversion of a sparse matrix into its corresponding MPO form, which is up to 509 times faster than the standard Tensor Train SVD (TTSVD) method while achieving machine precision accuracy. The efficiency and accuracy of both algorithms are demonstrated in numerical experiments.
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