TY - CHAP
A1 - Adm, Mohammad
A1 - Garloff, Jürgen
A1 - Titi, Jihad
T1 - Intervals of sign regular matrices
T2 - In: 8th Small Workshop in Interval Methods (SWIM 2015)
June 9 - 11, 2015, Prague, ISBN: 978-80-7378-293-1
IUUK-CE-ITI series ; 2015-620
KW - Interval matrix
KW - Checkerboard ordering
KW - Totally nonnegative matrix
KW - Sign regular matrix
Y1 - 2015
U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:bsz:kon4-opus4-6979
UR - https://iti.mff.cuni.cz/series/2015.html
SP - 1
EP - 4
ER -
TY - JOUR
A1 - Adm, Mohammad
A1 - Garloff, Jürgen
T1 - Intervals of special sign regular matrices
JF - Linear and Multilinear Algebra
N2 - We consider classes of n-by-n sign regular matrices, i.e., of matrices with the property that all their minors of fixed order k have one specified sign or are allowed also to vanish, k = 1, ... ,n. If the sign is nonpositive for all k, such a matrix is called totally nonpositive. The application of the Cauchon algorithm to nonsingular totally nonpositive matrices is investigated and a new determinantal test for these matrices is derived. Also matrix intervals with respect to the checkerboard partial ordering are considered. This order is obtained from the usual entry-wise ordering on the set of the n-by-n matrices by reversing the inequality sign for each entry in a checkerboard fashion. For some classes of sign regular matrices it is shown that if the two bound matrices of such a matrix interval are both in the same class then all matrices lying between these two bound matrices are in the same class, too.
KW - Sign regular matrix
KW - Totally nonnegative matrix
KW - Totally nonpositve matrix
KW - Cauchon algorithm
KW - Checkerboard ordering
Y1 - 2016
U6 - http://dx.doi.org/10.1080/03081087.2015.1090388
SN - 0308-1087
VL - 64
IS - 7
SP - 1424
EP - 1444
ER -
TY - THES
A1 - Adm, Mohammad
T1 - Perturbation and intervals of totally nonnegative matrices and related properties of sign regular matrices
KW - Totally nonnegative matrix
KW - Totally positive matrix
KW - Totally nonpositive matrix
KW - Sign regular matrix
KW - Cauchon algorithm
Y1 - 2016
U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:bsz:352-0-334132
UR - https://kops.uni-konstanz.de/handle/123456789/33829
ER -