Type of Publication:  Journal article 
Author:  Adm, Mohammad; Garloff, Jürgen; Titi, Jihad 
Year of publication:  2016 
Published in:  Journal of Mathematical Analysis and Applications ; 434 (2016), 1.  pp. 780797.  ISSN 0022247X.  eISSN 10960813 
DOI (citable link):  https://dx.doi.org/10.1016/j.jmaa.2015.08.078 
Summary: 
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. Rfunctions, 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.

Subject (DDC):  510 Mathematics 
Keywords:  Totally nonnegative matrix, totally positive matrix, Hurwitz matrix, Hankel matrix, Rfunction, interval polynomial 
Bibliography of Konstanz:  Yes 
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ADM, Mohammad, Jürgen GARLOFF, Jihad TITI, 2016. Total nonnegativity of matrices related to polynomial roots and poles of rational functions. In: Journal of Mathematical Analysis and Applications. 434(1), pp. 780797. ISSN 0022247X. eISSN 10960813. Available under: doi: 10.1016/j.jmaa.2015.08.078
@article{Adm201602Total31928, title={Total nonnegativity of matrices related to polynomial roots and poles of rational functions}, year={2016}, doi={10.1016/j.jmaa.2015.08.078}, number={1}, volume={434}, issn={0022247X}, journal={Journal of Mathematical Analysis and Applications}, pages={780797}, author={Adm, Mohammad and Garloff, Jürgen and Titi, Jihad} }
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