期刊
COMPUTATIONAL & APPLIED MATHEMATICS
卷 38, 期 3, 页码 -出版社
SPRINGER HEIDELBERG
DOI: 10.1007/s40314-019-0893-6
关键词
Moore-Penrose inverse; condition number; Perturbation bound; Tensor; Einstein product
The spectral norm of an even-order tensor is defined and investigated. An equivalence between the spectral norm of tensors and matrices is given. Using derived representations of some tensor expressions involving the Moore-Penrose inverse, we investigate the perturbation theory for the Moore-Penrose inverse of tensor via Einstein product. The classical results derived by Stewart (SIAM Rev 19:634-662, 1977) and Wedin (BIT 13:217-232, 1973) for the matrix case are extended to even-order tensors. An implementation in the Matlab programming language is developed and used in deriving appropriate numerical examples.
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