The model matching problem ${\bf min}_{R(z)}\|W(z)−R(z)E(z)\|_\infty$ involved in multirate filter banks design is addressed. A method is presented to design the synthesis filter bank $R(z)$ with the order of $W(z)$ which is the polyphase representation of the time delay of the reconstructed signal. The existence conditions of such low−order $R(z)$ are given in linear matrix inequalities (LMIs)...

For given matrix A ∈ Zd×n, the set Pb = { z : Az = b, z ∈ Z+ } describes the preimage or fiber of b ∈ Z under the Z-linear map fA : Z+ → Z, x 7→ Ax. The fiber Pb is called atomic if it has no nontrivial Minkowski decomposition, that is, Pb = Pb1 +Pb2 implies b = b1 or b = b2. In this paper we present a novel algorithm to compute such atomic fibers. An algorithmic solution to subproblems, comput...

zygophyllum atriplicoides is one of the important species of iran rangelands that has special importance owing to some properties like high distribution rate, coverage percentage, density, and plant biomass that make it possible to supply a part of forage needed by livestock during spring and winter as well as to avoid soil degradation against water and wind erosions. this research tries to stu...

Let Q(z, w) = − ∏n k=1[(z − ak)(w̄ − āk) − R]. The main result of the paper states that in the case when the nodes aj are situated at the vertices of a regular n-gon inscribed in the unit circle, the matrix Q(ai, aj) is positive definite if and only if R < ρn, where z = 2ρ 2 n − 1 is the smallest 6= −1 zero of the Jacobi polynomial Pn−2ν,−1 ν (z), ν = [n/2].

Let Z and R be the sets of all integers and real numbers, respectively. For a,b ∈ Z, define Z(a)= {a,a+1, . . .} and Z(a,b)= {a,a+1, . . . ,b} when a≤ b. Let A be an n×m matrix. Aτ denotes the transpose ofA.When n=m, σ(A) and det(A) denote the set of eigenvalues and the determinant of A, respectively. In this paper, we study the existence of multiple p-periodic solutions to the following discre...

Abstract: Easily computable recursive algorithms are proposed for estimating coefficients of A(z), C(z), and the covariance matrix Rw of wk for the multivariate ARMA process A(z)yk = C(z)wk on the basis of the noise-corrupted observations ηk ∆ = yk + ǫk. It is shown that the estimates converge to the true ones under reasonable conditions. An illustrative example is provided, and the simulation ...

A wave function of the N -component KP Hierarchy with continuous flows determined by an invertible matrix H is constructed from the choice of an MN -dimensional space of finitely-supported vector distributions. This wave function is shown to be an eigenfunction for a ring of matrix differential operators in x having eigenvalues that are matrix functions of the spectral parameter z. If the space...

Let Z and R be the sets of all integers and real numbers, respectively. For a,b ∈ Z, define Z(a)= {a,a+1, . . .} and Z(a,b)= {a,a+1, . . . ,b} when a≤ b. Let A be an n×m matrix. Aτ denotes the transpose ofA.When n=m, σ(A) and det(A) denote the set of eigenvalues and the determinant of A, respectively. In this paper, we study the existence of multiple p-periodic solutions to the following discre...

A large class of teletraac problems are based on Markov chains of M/G/1 and G/M/1 type, the study of which requires numerically eecient and reliable algorithms to solve the nonlinear matrix equations arising in such chains. Given A i ; i 0, a sequence of square m-by-m nonnegative matrices and A(z) = P 1 i=0 A i z i with A(1) being an irreducible stochastic matrix, these equations for M/G/1 type...

classes of‎ ‎abaffy-broyden-spedicato (abs) methods have been introduced for‎ ‎solving linear systems of equations‎. ‎the algorithms are powerful methods for developing matrix‎ ‎factorizations and many fundamental numerical linear algebra processes‎. ‎here‎, ‎we show how to apply the abs algorithms to devise algorithms to compute the wz and zw‎ ‎factorizations of a nonsingular matrix as well as...