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Perturbations of Tensor-Schur decomposition and its applications to multilinear control systems and facial recognitions.
- Source :
-
Neurocomputing . Aug2023, Vol. 547, pN.PAG-N.PAG. 1p. - Publication Year :
- 2023
-
Abstract
- Perturbation analysis has been primarily considered to be one of the main issues in many fields. The Schur decomposition can factor a square matrix as the product of a unitary matrix and an upper triangular matrix, which contains eigenvalues of the square matrix. In view of the importance of T-eigenvalue problems, this paper discusses a tensor Schur decomposition (T-Schur), the T-Schur decomposition = U ∗ T ∗ U ∗ , which is based on T-product multiplication of third-order tensors. We present the normwise and componentwise perturbation analysis for the unitary tensor U , the upper triangular tensor T and T-eigenvalues of the tensor A. We explore some applications of the T-Schur decomposition and perform the T-Schur form to solve the tensor pole assignment. We give an algorithm to solve the tensor based T-Sylvester equation and present its perturbation bound and the backward error. The T-Sylvester equation can also be used to estimate the condition of the T-sign function. We apply the T-Schur decomposition to facial recognation and compare it with other types of tensor decompositions. [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 09252312
- Volume :
- 547
- Database :
- Academic Search Index
- Journal :
- Neurocomputing
- Publication Type :
- Academic Journal
- Accession number :
- 164301802
- Full Text :
- https://doi.org/10.1016/j.neucom.2023.126359