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 -