期刊
NUMERICAL LINEAR ALGEBRA WITH APPLICATIONS
卷 27, 期 3, 页码 -出版社
WILEY
DOI: 10.1002/nla.2288
关键词
block circulant matrices; matrix functions; multidimensional arrays; network analysis; tensor t-product; tensors
资金
- U.S. National Science Foundation [DMS-14188822]
- U.S. Department of Energy [DE-SC 00165783]
- Charles University, PRIMUS grant [PRIMUS/19/SCI/11]
A definition for functions of multidimensional arrays is presented. The definition is valid for third-order tensors in the tensor t-product formalism, which regards third-order tensors as block circulant matrices. The tensor function definition is shown to have similar properties as standard matrix function definitions in fundamental scenarios. To demonstrate the definition's potential in applications, the notion of network communicability is generalized to third-order tensors and computed for a small-scale example via block Krylov subspace methods for matrix functions. A complexity analysis for these methods in the context of tensors is also provided.
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