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- W4300716779 abstract "The paper is concerned with methods for computing the best low multilinear rank approximation of large and sparse tensors. Krylov-type methods have been used for this problem; here block versions are introduced. For the computation of partial eigenvalue and singular value decompositions of matrices the Krylov-Schur (restarted Arnoldi) method is used. We describe a generalization of this method to tensors, for computing the best low multilinear rank approximation of large and sparse tensors. In analogy to the matrix case, the large tensor is only accessed in multiplications between the tensor and blocks of vectors, thus avoiding excessive memory usage. It is proved that, if the starting approximation is good enough, then the tensor Krylov-Schur method is convergent. Numerical examples are given for synthetic tensors and sparse tensors from applications, which demonstrate that for most large problems the Krylov-Schur method converges faster and more robustly than higher order orthogonal iteration." @default.
- W4300716779 created "2022-10-04" @default.
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- W4300716779 date "2020-12-14" @default.
- W4300716779 modified "2023-09-27" @default.
- W4300716779 title "A Krylov-Schur like method for computing the best rank-$(r_1,r_2,r_3)$ approximation of large and sparse tensors" @default.
- W4300716779 doi "https://doi.org/10.48550/arxiv.2012.07595" @default.
- W4300716779 hasPublicationYear "2020" @default.
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