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Total Nonnegativity of Matrices Related to Polynomial Roots and Poles of Rational Functions

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dc.contributor.author Adm, Mohammad
dc.contributor.author Garloff, Juergen
dc.contributor.author Titi, Jihad
dc.date.accessioned 2017-02-01T07:22:06Z
dc.date.accessioned 2022-05-22T08:27:46Z
dc.date.available 2017-02-01T07:22:06Z
dc.date.available 2022-05-22T08:27:46Z
dc.date.issued 2016
dc.identifier.uri http://localhost:8080/xmlui/handle/123456789/7831
dc.description.abstract In this paper totally nonnegative (positive) matrices are considered which are matrices having all their minors nonnegative (positive); 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. en_US
dc.language.iso en en_US
dc.publisher Journal of Mathematical Analysis and Applications en_US
dc.subject Totally nonnegative matrix, Totally positive matrix, Hurwitz matrix, Hankel matrix, R-function, Interval polynomial en_US
dc.title Total Nonnegativity of Matrices Related to Polynomial Roots and Poles of Rational Functions en_US

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