TY - JOUR
T1 - The totally non-positive matrix completion problem
AU - J. P. Liang & M. He 
JO - Numerical Mathematics, a Journal of Chinese Universities
VL - 4
SP - 312
EP - 319
PY - 2006
DA - 2006/11
SN - 15
DO - http://doi.org/
UR - https://global-sci.org/intro/article_detail/nm/8039.html
KW - 
AB - 
In this paper, the totally non-positive matrix is introduced. The
totally non-positive completion asks which partial totally
non-positive matrices have a completion to a totally non-positive
matrix. This problem has, in general, a negative answer. Therefore,
our question is for what kind of labeled graphs $G$ each partial
totally non-positive matrix whose associated graph is $G$ has a
totally non-positive completion? If $G$ is not a monotonically
labeled graph or monotonically labeled cycle, we give necessary and
sufficient conditions that guarantee the existence of the desired
completion.