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    Wyświetlanie 1-3 z 3
    Tytuł:
    Factorization of Nonnegative Matrices by the Use of Elementary Operation
    Autorzy:
    Kaczorek, T.
    Powiązania:
    https://bibliotekanauki.pl/articles/386810.pdf
    Data publikacji:
    2012
    Wydawca:
    Politechnika Białostocka. Oficyna Wydawnicza Politechniki Białostockiej
    Tematy:
    faktoryzacja
    nieujemna macierz
    procedura
    obliczanie
    factorization
    nonnegative matrix
    positive rank
    procedure
    computation
    Opis:
    A method based on elementary column and row operations of the factorization of nonnegative matrices is proposed. It is shown that the nonnegative matrix R×( ? ) has positive full column rank if and only if it can be transformed to a matrix with cyclicstructure. A procedure for computation of nonnegative matrices ? R ×, ? R × ( ? rank (,)) satisfying = is proposed.
    Źródło:
    Acta Mechanica et Automatica; 2012, 6, 4; 15-18
    1898-4088
    2300-5319
    Pojawia się w:
    Acta Mechanica et Automatica
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Stability and stabilization of positive linear dynamical systems: new equivalent conditions and computations
    Autorzy:
    Yang, H.
    Hu, Y.
    Powiązania:
    https://bibliotekanauki.pl/articles/201932.pdf
    Data publikacji:
    2020
    Wydawca:
    Polska Akademia Nauk. Czytelnia Czasopism PAN
    Tematy:
    positive linear systems
    stability
    stabilization
    linear inequalities systems
    consistency
    I-rank
    Opis:
    New equivalent conditions of the asymptotical stability and stabilization of positive linear dynamical systems are investigated in this paper. The asymptotical stability of the positive linear systems means that there is a solution for linear inequalities systems. New necessary and sufficient conditions for the existence of solutions of the linear inequalities systems as well as the asymptotical stability of the linear dynamical systems are obtained. New conditions for the stabilization of the resultant closed-loop systems to be asymptotically stable and positive are also presented. Both the stability and the stabilization conditions can be easily checked by the so-called I-rank of a matrix and by solving linear programming (LP). The proposed LP has compact form and is ready to be implemented, which can be considered as an improvement of existing LP methods. Numerical examples are provided in the end to show the effectiveness of the proposed method.
    Źródło:
    Bulletin of the Polish Academy of Sciences. Technical Sciences; 2020, 68, 2; 307-315
    0239-7528
    Pojawia się w:
    Bulletin of the Polish Academy of Sciences. Technical Sciences
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    A linear programming based analysis of the CP-rank of completely positive matrices
    Autorzy:
    Li, Y.
    Kummert, A.
    Frommer, A.
    Powiązania:
    https://bibliotekanauki.pl/articles/907323.pdf
    Data publikacji:
    2004
    Wydawca:
    Uniwersytet Zielonogórski. Oficyna Wydawnicza
    Tematy:
    macierz pozytywna
    programowanie liniowe
    algorytm Simplex
    completely positive matrices
    cp-rank
    linear programming
    simplex algorithm
    basic feasible solution
    pivot process
    Opis:
    A real matrix A is said to be completely positive (CP) if it can be decomposed as A= B BT, where the real matrix B has exclusively non-negative entries. Let k be the rank of A and Phik the least possible number of columns of the matrix B, the so-called completely positive rank (cp-rank) of A. The present work is devoted to a study of a general upper bound for the cp-rank of an arbitrary completely positive matrix A and its dependence on the ordinary rank k. This general upper bound of the cp-rank has been proved to be at most k(k + 1)/2. In a recent pioneering work of Barioli and Berman it was slightly reduced by one, which means that Phik \leq k(k + 1)/2-1 holds for k \geq 2. An alternative constructive proof of the same result is given in the present paper based on the properties of the simplex algorithm known from linear programming. Our proof illuminates complete positivity from a different point of view. Discussions concerning dual cones are not needed here. In addition to that, the proof is of constructive nature, i.e. starting from an arbitrary decomposition A= B1 B1T (B1\geq 0) a new decomposition A= B2 B2T (B2\geq 0) can be generated in a constructive manner, where the number of column vectors of B2 does not exceed k(k + 1)/2-1. This algorithm is based mainly on the well-known techniques stemming from linear programming, where the pivot step of the simplex algorithm plays a key role.
    Źródło:
    International Journal of Applied Mathematics and Computer Science; 2004, 14, 1; 25-31
    1641-876X
    2083-8492
    Pojawia się w:
    International Journal of Applied Mathematics and Computer Science
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
      Wyświetlanie 1-3 z 3

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