Two fast numerical algorithms are proposed for computing interval vectors containing positive solutions to M-tensor multi-linear systems. The first algorithm involves only two tensor-vector multiplications. The second algorithm is iterative one, and generally gives interval vectors narrower than those by the first algorithm. Numerical results show efficiency of the algorithms.
Topics
Numerical algorithms
REFERENCES
1.
W.
Ding
and Y.
Wei
, “Solving multi-linear systems with M-tensors”, J. Sci. Comput.
68
(2
), 689
–715
(2016
).2.
L. -B.
Cui
, X. -Q
. Zhang
, and S. -L
. Wu
, “A new preconditioner of the tensor splitting iterative method for solving multi-linear systems with M-tensors
”, Comput. Appl. Math.
39
, 173
(2020
).3.
W.
Li
, D.
Liu
, and S. -W.
Vong
, “Comparison results for splitting iterations for solving multi-linear systems
”, Appl. Numer. Math.
134
, 105
–121
(2018
).4.
D.
Liu
, W.
Li
, and S. -W.
Vong
, “A new preconditioned SOR method for solving multi-linear systems with an M-tensor
”, Calcolo
57
, 15
(2020
).5.
R.
Krawczyk
, “Newton-Algorithmen zur Bestimmung von Nullstellen mit Fehlerschranken”, Computing
4
, 187
–201
(1969
).6.
S. M.
Rump
, “INTLAB - INTerval LABoratory”, in Developments in Reliable Computing
, edited by T.
Csendes
(Kluwer Academic Publishers
, Dordrecht
, 1999
), pp. 77
–104
.
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