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Noda iteration for computing generalized tensor eigenpairs.
- Source :
-
Journal of Computational & Applied Mathematics . Nov2023, Vol. 432, pN.PAG-N.PAG. 1p. - Publication Year :
- 2023
-
Abstract
- In this paper, we propose the tensor Noda iteration (NI) and its inexact version for solving the eigenvalue problem of a particular class of tensor pairs called generalized M -tensor pairs. A generalized M -tensor pair consists of a weakly irreducible nonnegative tensor and a nonsingular M -tensor within a linear combination. It is shown that any generalized M -tensor pair admits a unique positive generalized eigenvalue with a positive eigenvector. A modified tensor Noda iteration (MTNI) is developed for extending the Noda iteration for nonnegative matrix eigenproblems. In addition, the inexact generalized tensor Noda iteration method (IGTNI) and the generalized Newton-Noda iteration method (GNNI) are also introduced for more efficient implementations and faster convergence. Under a mild assumption on the initial values, the convergence of these algorithms is guaranteed. The efficiency of these algorithms is illustrated by numerical experiments. [ABSTRACT FROM AUTHOR]
- Subjects :
- *NONNEGATIVE matrices
*NEWTON-Raphson method
*PROBLEM solving
*EIGENVALUES
Subjects
Details
- Language :
- English
- ISSN :
- 03770427
- Volume :
- 432
- Database :
- Academic Search Index
- Journal :
- Journal of Computational & Applied Mathematics
- Publication Type :
- Academic Journal
- Accession number :
- 163891135
- Full Text :
- https://doi.org/10.1016/j.cam.2023.115284