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Browsing by Author "Adm, Mohammad"

Browsing by Author "Adm, Mohammad"

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  • Bounding the Range of a Sum of Multivariate Rational Functions 
    Adm, Mohammad; Garloff, Juergen; Titi, Jihad; Elgayar, Ali (Springer, 2022)
    Bounding the range of a sum of rational functions is an important task if, e.g., the global polynomial sum of ratios problem is solved by a branch and bound algorithm. In this paper, bounding methods are discussed which ...
  • Bounding the Range of a Sum of Multivariate Rational Functions 
    Adm, Mohammad; Titi, Jihad; Elgayar, Ali; Garloff, Jürgen (in M. Ceberio and V. Kreinovich (eds.), Decision Making under Uncertainty and Constraints, Studies in Systems, Decision and Control 217, Springer Nature, 2023)
    Bounding the range of a sum of rational functions is an important task if, e.g., the global polynomial sum of ratios problem is solved by a branch and bound algorithm. In this paper, bounding methods are discussed which ...
  • Bounds and majorization relations for the critical points of polynomials 
    Adm, Mohammad; Kittaneh, Fuad (Linear Algebra and its Applications, 2012-04-01)
    We apply several matrix inequalities to the derivative companion matrices of complex polynomials to establish new bounds and majorization relations for the critical points of these polynomials in terms of their zeros.
  • Characterization, perturbation, and interval property of certain sign regular matrices 
    Adm, Mohammad; Garloff, Jürgen (Linear Algebra and its Applications Journal, 2021-03-01)
    The class of square matrices of order n having a negative determinant and all their minors up to order n-1 nonnegative is considered. A characterization of these matrices is presented which provides an easy test based on ...
  • Further Matrix Classes Possessing the Interval Property 
    Garloff, Juergen; Al-Saafin, Doaa; Adm, Mohammad (Reliable Computing (Interval Computations) Journal, 2021)
    In this article, the collection of classes of matrices which possess the interval property presented in [J. Garloff, M. Adm, and J. Titi, A survey of classes of matrices possessing the interval property and related prop- ...
  • Improved Tests and Characterizations of Totally Nonnegative Matrices 
    Adm, Mohammad; Garloff, Juergen (Electronic Journal of Linear Algebra, 2014)
    Totally nonnegative matrices, i.e., matrices having all minors nonnegative, are considered. A condensed form of the Cauchon algorithm which has been proposed for finding a parameterization of the set of these matrices with ...
  • Intervals of Special Sign Regular Matrices 
    Adm, Mohammad; Garloff, Juergen (Linear and Multilinear Algebra, 2016)
    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 ...
  • Intervals of Totally Nonnegative Matrices 
    Adm, Mohammad; Garloff, Juergen (Linear Algebra and its Applications, 2013)
    Totally nonnegative matrices, i.e., matrices having all their minors nonnegative, and matrix intervals with respect to the checkerboard ordering are considered. It is proven that if the two bound matrices of such a matrix ...
  • Invariance of total nonnegativity of a matrix under entry-wise perturbation and subdirect sum of totally nonnegative matrices 
    Adm, Mohammad; Garloff, Jürgen (Linear Algebra and its Applications Journal, 2017-02-01)
    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, ...
  • Invariance of Total Nonnegativity of a Tridiagonal Matrix under Element-wise Perturbation 
    Adm, Mohammad; Garloff, Juergen (Operators and Matrices, 2014-03-01)
    Tridiagonal matrices are considered which are totally nonnegative, i. e., all their minors are nonnegative. The largest amount is given by which the single entries of such a matrix can be perturbed without losing the ...
  • Invariance of Total Positivity of a Matrix under Entry-wise Perturbation and Completion Problems 
    Adm, Mohammad; Garloff, Juergen (In: A Panorama of Mathematics: Pure and Applied, Contemporary Mathematics, vol. 658, Amer. Math. Soc.,, 2016)
    A totally positive matrix is a matrix having all its minors positive. The largest amount by which the single entries of such a matrix can be perturbed without losing the property of total positivity is given. Also some ...
  • Linear Algebra and its Applications 
    Adm, Mohammad; Al Muhtaseb, Khawla; Abedel Ghani, Ayed; Fallat, Shaun; Garlof, Jürgen (Elsevier Inc., 2018-02-02)
    For a class of matrices connected with Cauchon diagrams, Cauchon matrices, and the Cauchon algorithm, a method for determining the rank, and for checking a set of consecutive row (or column) vectors for linear independence ...
  • Relaxing the Nonsingularity Assumption for Intervals of Totally Nonnegative Matrices 
    Adm, Mohammad; Almuhtaseb, Khawla; Abedel Ghani, Ayed; Garloff, Jürgen (Electronic Journal of Linear Algebra, 2020-03-27)
    Totally nonnegative matrices, i.e., matrices having all their minors nonnegative, and matrix intervals with respect to the checkerboard partial order are considered. It is proven that if the two bound matrices of such a ...
  • A Survey of Classes of Matrices Possessing the Interval Property and Related Properties 
    Adm, Mohammad; Garloff, Juergen; Titi, Jihad (Reliable Computing, 2016)
    This paper considers intervals of real matrices with respect to partial orders and the problem to infer from some exposed matrices lying on the boundary of such an interval that all real matrices taken from the interval ...
  • Total Nonnegativity of Matrices Related to Polynomial Roots and Poles of Rational Functions 
    Adm, Mohammad; Garloff, Juergen; Titi, Jihad (Journal of Mathematical Analysis and Applications, 2016)
    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 ...
  • Total nonnegativity of the extended Perron complement 
    Adm, Mohammad; Garloff, Jürgen (Linear Algebra Appl., 2016-11-01)
    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 ...
  • Weakly Hadamard diagonalizable graphs 
    Adm, Mohammad; Almuhtaseb, Khawla; Fallat, Shaun; Meagher, Karen; Nasserasr, Shahla; Shirazi, Mahsa; Razafimahatratra, A. S. (Linear Algebra and its Applications Journal, 2021-02-01)
    A matrix is called weakly Hadamard if its entries are from {0, -1, 1} and its non-consecutive columns (with some ordering) are orthogonal. Unlike Hadamard matrices, there is a weakly Hadamard matrix of order n for every ...

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