@inproceedings{AdmGarloffTiti,
author = {Adm, Mohammad and Garloff, J{\"u}rgen and Titi, Jihad},
title = {Intervals of sign regular matrices},
series = {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},
url = {http://nbn-resolving.de/urn:nbn:de:bsz:kon4-opus4-6979},
pages = {1 -- 4},
language = {en}
}
@article{AdmGarloff,
author = {Adm, Mohammad and Garloff, J{\"u}rgen},
title = {Intervals of special sign regular matrices},
series = {Linear and Multilinear Algebra},
volume = {64},
number = {7},
issn = {0308-1087},
doi = {10.1080/03081087.2015.1090388},
pages = {1424 -- 1444},
abstract = {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.},
language = {de}
}
@phdthesis{Adm,
author = {Adm, Mohammad},
title = {Perturbation and intervals of totally nonnegative matrices and related properties of sign regular matrices},
url = {http://nbn-resolving.de/urn:nbn:de:bsz:352-0-334132},
pages = {189},
language = {en}
}