We propose a numerical algorithm for computing interval vectors containing Perron vectors of a kind of weakly irre-ducible nonnegative tensors, which we call slightly positive tensors. This algorithm involves only two tensor-vector multiplications. Numerical results show efficiency of the algorithm.
Topics
Numerical algorithms
REFERENCES
1.
L.
Qi
and Z.
Luo
, Tensor Analysis: Spectral Theory and Special Tensors
(SIAM Publications
, Philadelphia
, 2017
).2.
W.
Ding
and Y.
Wei
, “Solving multi-linear systems with M-tensors
”, J. Sci. Comput.
68
(2
), 689
–715
(2016
).3.
R.
Krawczyk
, “Newton-Algorithmen zur Bestimmung von Nullstellen mit Fehlerschranken
”, Computing
4
, 187
–201
(1969
).4.
S. M.
Rump
, “INTLAB - INTerval LABoratory”, in Developments in Reliable Computing
, edited by T.
Csendes
(Kluwer Academic Publishers
, Dordrecht
, 1999
), pp. 77
–104
.5.
Y.
Liu
, G.
Zhou
, and N. F.
Ibrahim
, “An always convergent algorithm for the largest eigenvalue of an irre-ducible nonnegative tensor
”, J. Comput. Appl. Math.
235
, 286
–292
(2010
).6.
L.
Zhang
, L.
Qi
, and Y.
Xu
, “Linear convergence of the LZI algorithm for weakly positive tensors
”, J. Comput. Math.
30
(1
), 24
–33
(2012
).
This content is only available via PDF.
©2023 Authors. Published by AIP Publishing.
2023
Author(s)
You do not currently have access to this content.