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.

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
.
This content is only available via PDF.
You do not currently have access to this content.