TY - CHAP
A1 - Garloff, Jürgen
A1 - Adm, Mohammad
A1 - Al Muhtaseb, Khawla
A1 - Ghani, Ayed Abedel
T1 - Relaxing the nonsingularity assumption for intervals of totally nonnegative matrices
T2 - MAT TRIAD 2019 Book of Abtracts, International Conference on Matrix Analysis and its Applications, September 8-13, Liblice, Czech Republic (IUUK-CE-ITI series 2019)
Y1 - 2019
UR - https://mattriad.math.cas.cz//programme/
SP - 23
EP - 23
ER -
TY - CHAP
A1 - Adm, Mohammad
A1 - Garloff, Jürgen
T1 - Recent applications of the Cauchon algorithm to the totally nonnegative matrices
T2 - Meeting of the International Linear Algebra Society (ILAS 2017: Connections), Ames, Iowa State University, July 24-28 2017
Y1 - 2017
ER -
TY - CHAP
A1 - Adm, Mohammad
A1 - Garloff, Jürgen
T1 - A novel method for determining the rank of a matrix
T2 - Special Western Canada Linear Algebra Meeting, Banff International Research Station for Mathematical Innovation and Discovery, Banff, Alberta, Canada, July 7-9th 2017
N2 - Presentation
Y1 - 2017
ER -
TY - CHAP
A1 - Adm, Mohammad
A1 - Garloff, Jürgen
T1 - Efficient determinantal tests for sign regular matrices
T2 - Proceedings of the 14th Pacific Institute for the Mathematical Sciences Young Researchers Conference, University of Saskatchewan, Saskatoon, Canada, June 5-8th 207
Y1 - 2017
SP - 11
EP - 12
ER -
TY - CHAP
A1 - Adm, Mohammad
A1 - Garloff, Jürgen
T1 - Optimal determinantal criteria for and intervals of totally nonnegative matrices
T2 - The Prairie Discrete Math Workshop (PDMW 2017), 2–5 June, 2017, Living Skies Conference Centre Lumsden, Saskatchewan, Canada
Y1 - 2017
SP - 3
EP - 4
ER -
TY - GEN
A1 - Adm, Mohammad
T1 - Some stability criteria for polynomials and interval polynomials
N2 - Vortrag auf dem Doktorandenkolloquium des Kooperativen Promotionskollegs der HTWG, 09.07.2015
Y1 - 2015
ER -
TY - JOUR
A1 - Adm, Mohammad
A1 - Garloff, Jürgen
T1 - Invariance of total nonnegativity of a matrix under entry-wise perturbation and subdirect sum of totally nonnegative matrices
JF - Linear Algebra and its Applications
N2 - A real matrix is called totally nonnegative if all of its minors are nonnegative. In this paper, the minors are determined from which the maximum allowable entry perturbation of a totally nonnegative matrix can be found, such that the perturbed matrix remains totally nonnegative. Also, the total nonnegativity of the first and second subdirect sum of two totally nonnegative matrices is considered.
KW - Totally nonnegative matrix
KW - Entry-wise perturbation
KW - K-subdirect sum
Y1 - 2017
UR - https://www.sciencedirect.com/science/article/pii/S0024379516305171
U6 - http://dx.doi.org/10.1016/j.laa.2016.11.001
SN - 0024-3795
N1 - Volltextzugriff für Angehörige der Hochschule Konstanz möglich.
VL - 2017
IS - 514
SP - 222
EP - 233
ER -
TY - JOUR
A1 - Adm, Mohammad
A1 - Garloff, Jürgen
T1 - Total nonnegativity of matrices related to polynomial roots and poles of rational functions
JF - Journal of Mathematical Analysis and Applications
N2 - In this paper totally nonnegative (positive) matrices are considered which are matrices having all their minors nonnegative (positve); the almost totally positive matrices form a class between the totally nonnegative matrices and the totally positive ones. An efficient determinantal test based on the Cauchon algorithm for checking a given matrix for falling in one of these three classes of matrices is applied to matrices which are related to roots of polynomials and poles of rational functions, specifically the Hankel matrix associated with the Laurent series at infinity of a rational function and matrices of Hurwitz type associated with polynomials. In both cases it is concluded from properties of one or two finite sections of the infinite matrix that the infinite matrix itself has these or related properties. Then the results are applied to derive a sufficient condition for the Hurwitz stability of an interval family of polynomials. Finally, interval problems for a subclass of the rational functions, viz. R-functions, are investigated. These problems include invariance of exclusively positive poles and exclusively negative roots in the presence of variation of the coefficients of the polynomials within given intervals.
KW - Totally nonnegative matrix
KW - Totally positive matrix
KW - Hurwitz matrix
KW - Hankel matrix
KW - R-function
Y1 - 2016
UR - https://www.sciencedirect.com/journal/journal-of-mathematical-analysis-and-applications/vol/434/issue/1
SN - 0022-247X
SN - 1096-0813
VL - 434
IS - 1
SP - 780
EP - 797
ER -
TY - JOUR
A1 - Adm, Mohammad
A1 - Garloff, Jürgen
T1 - Total nonnegativity of the extended Perron complement
JF - Linear Algebra and its Applications
N2 - A real matrix is called totally nonnegative if all of its minors are nonnegative. In this paper the extended Perron complement of a principal submatrix in a matrix A is investigated. In extension of known results it is shown that if A is irreducible and totally nonnegative and the principal submatrix consists of some specified consecutive rows then the extended Perron complement is totally nonnegative. Also inequalities between minors of the extended Perron complement and the Schur complement are presented.
KW - Totally nonnegative matrix
KW - Perron complement
KW - Extended Perron complement
KW - Schur complement
Y1 - 2016
UR - http://nbn-resolving.de/urn:nbn:de:bsz:352-0-386980
U6 - http://dx.doi.org/10.1016/j.laa.2016.07.002
SN - 0024-3795
SN - 1873-1856
IS - 508
SP - 214
EP - 224
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 -