‎the global generalized minimum residual (gl-gmres)‎ ‎method is examined for solving the generalized sylvester matrix equation‎ ‎[sumlimits_{i = 1}^q {a_i } xb_i = c.]‎ ‎some new theoretical results are elaborated for‎ ‎the proposed method by employing the schur complement‎. ‎these results can be exploited to establish new convergence properties‎ ‎of the gl-gmres method for solving genera...

Matrix-valued analogues of the little q-Jacobi polynomials are introduced and studied. For the 2 × 2-matrix-valued little q-Jacobi polynomials explicit expressions for the orthogonality relations, Rodrigues formula, three-term recurrence relation and its relation to matrix-valued q-hypergeometric series and the scalar-valued little q-Jacobi polynomials are presented. The study is based on the m...

Abstract. A real n × n matrix is a Q-matrix if for every k = 1, 2, . . . , n the sum of all k × k principal minors is positive. A digraph D is said to have Q-completion if every partial Q-matrix specifying D can be completed to a Q-matrix. For the Q-completion problem, sufficient conditions for a digraph to have Q-completion are given, necessary conditions for a digraph to have Q-completion are...

A generalized q-Pilbert matrix from [2] is further generalized, introducing one additional parameter. Explicit formulæ are derived for the LU-decomposition and their inverses, as well as the Cholesky decomposition. The approach is to use q-analysis and to leave the justification of the necessary identities to the q-version of Zeilberger’s celebrated algorithm. However, the necessary identities ...

In this paper, the nonnegative Q-matrix completion problem is studied. A real n × n matrix is a Q-matrix if for k ∈ {1, . . . , n}, the sum of all k × k principal minors is positive. A digraph D is said to have nonnegative Q-completion if every partial nonnegative Q-matrix specifying D can be completed to a nonnegative Q-matrix. For nonnegative Q-completion problem, necessary conditions and suf...