共查询到20条相似文献,搜索用时 46 毫秒
1.
《数学季刊》2016,(1):60-68
Under the assumption that the wiretapper can get at most r(r n) independent messages, Cai et al. showed that any rate n multicast code can be modified to another secure network code with transmitting rate n- r by a properly chosen matrix Q~(-1). They also gave the construction for searching such an n × n nonsingular matrix Q. In this paper, we find that their method implies an efficient construction of Q. That is to say, Q can be taken as a special block lower triangular matrix with diagonal subblocks being the(n- r) ×(n- r)and r × r identity matrices, respectively. Moreover, complexity analysis is made to show the efficiency of the specific construction. 相似文献
2.
V. B. Larin 《Ukrainian Mathematical Journal》1987,39(1):42-45
The present paper gives an algorithm for the construction of the zeroth and first approximations of the solution of the algebraic matrix Riccati equation when the real part of the eigenvalues of the corresponding Hamiltonian matrix are much less than their imaginary parts. Unlike [1, 2] the basis of this algorithm is the construction of a transformation of the Hamiltonian matrix which conserves the eigenvectors of the matrix and changes its spectrum in the required direction (similar transformations were used in [3] to accelerate the convergence of the procedure for the construction of a matrix sign function).Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 39, No. 1, pp. 52–56, January–February, 1987. 相似文献
3.
Theodore J. Sheskin 《International Journal of Mathematical Education in Science & Technology》2013,44(5):799-805
We present a new matrix construction algorithm for computing absorption probabilities for a finite, reducible Markov chain. The construction algorithm contains two steps: matrix augmentation and matrix reduction. The algorithm requires more memory and less execution time than the calculation of absorption probabilities by the LU decomposition. We apply the algorithm to a Markovian model of a production line. 相似文献
4.
George Benke 《Journal of Fourier Analysis and Applications》1994,1(1):87-101
The classical Rudin–Shapiro construction produces a sequence of polynomials
with ±1 coefficients such that on the unit circle each such polynomial P satisfies the "flatness"
property ||P||∞ ≤ √2||P||2. It is shown how to construct blocks of such flat polynomials so that the polynomials in each block form an orthogonal system.
The construction depends on a fundamental generating matrix and a recursion rule. When the generating matrix is a multiple
of a unitary matrix, the flatness, orthogonality, and other symmetries are obtained. Two different recursion rules are examined
in detail and are shown to generate the same blocks of polynomials although with permuted orders. When the generating matrix
is the Fourier matrix, closed-form formulas for the polynomial coefficients are obtained. The connection with the Hadamard
matrix is also discussed. 相似文献
5.
(d,r)-disjunct矩阵、(d,r,z)-disjunct矩阵、(d,r,z]-disjunct矩阵等是一类d-disjunct矩阵,它们比d-disjunct矩阵有着更为广泛的应用.介绍了这一类d-disjunct矩阵的一种简单构作方法,并计算了它的参数. 相似文献
6.
7.
We construct infinite families of graphs that are determined by their generalized spectrum. This construction is based on new formulae for the determinant of the walk matrix of a graph. All graphs constructed here satisfy a certain extremal divisibility condition for the determinant of their walk matrix. 相似文献
8.
The paper develops construction procedures for tight framelets and wavelets using matrix mask functions in the setting of a generalized multiresolution analysis (GMRA). We show the existence of a scaling vector of a GMRA such that its first component exhausts the spectrum of the core space near the origin. The corresponding low-pass matrix mask has an especially advantageous form enabling an effective reconstruction procedure of the original scaling vector. We also prove a generalization of the Unitary Extension Principle for an infinite number of generators. This results in the construction scheme for tight framelets using low-pass and high-pass matrix masks generalizing the classical MRA constructions. We prove that our scheme is flexible enough to reconstruct all possible orthonormal wavelets. As an illustration we exhibit a pathwise connected class of non-MSF non-MRA wavelets sharing the same wavelet dimension function. 相似文献
9.
《Mathematical and Computer Modelling》2002,35(9-10):1061-1076
This paper deals with initial value problems for Lipschitz continuous coefficient matrix Riccati equations. Using Chebyshev polynomial matrix approximations the coefficients of the Riccati equation are approximated by matrix polynomials in a constructive way. Then using the Fröbenius method developed in [1], given an admissible error ϵ > 0 and the previously guaranteed existence domain, a rational matrix polynomial approximation is constructed so that the error is less than ϵ in all the existence domain. The approach is also considered for the construction of matrix polynomial approximations of nonhomogeneous linear differential systems avoiding the integration of the transition matrix of the associated homogeneous problem. 相似文献
10.
Thomas Johansson 《Designs, Codes and Cryptography》1994,4(1):69-81
We consider the authentication problem, using the model described by Simmons. Several codes have been constructed using combinatorial designs and finite geometries. We introduce a new way of constructing authentication codes using LFSR-sequences. A central part of the construction is an encoding matrix derived from these LFSR-sequences. Necessary criteria for this matrix in order to give authentication codes that provides protection aginst impersonation and substitution attacks will be given. These codes also provide perfect secrecy if the source states have a uniform distribution. Moreover, the codes give a natural splitting of the key into two parts, one part used aginst impersonation attacks and a second part used against substitution attacks and for secrecy simultaneously. Since the construction is based on the theory of LFSR-sequences it is very suitable for implementation and a simple implementation of the construction is given. 相似文献
11.
Christopher Storm 《Discrete Mathematics》2011,(14):1323
Recently, Storm used generating functions to provide a proof that an infinite family of graphs constructed by Cooper have the same Ihara zeta function. Here, we generalize the construction of that infinite family of graphs to a directed graph construction. A similar generating function proof technique applies, and we exhibit conditions under which our digraphs have the same spectra with respect to the adjacency matrix. 相似文献
12.
13.
S. M. Chuiko 《Russian Mathematics (Iz VUZ)》2018,62(4):74-85
We find solvability conditions and give a construction of generalized Green operator for a linear matrix boundary-value problem. We suggest an operator which reduces a linear matrix equation to a standard linearNoetherian boundary-value problem. To solve a linearmatrix systemwe use an operatorwhich reduces a linear matrix equation to a linear algebraic equation with rectangular matrix. 相似文献
14.
Antonio J. Durán 《Journal of Mathematical Analysis and Applications》2009,354(1):1-11
We show that any scalar differential operator with a family of polynomials as its common eigenfunctions leads canonically to a matrix differential operator with the same property. The construction of the corresponding family of matrix valued polynomials has been studied in [A. Durán, A generalization of Favard's theorem for polynomials satisfying a recurrence relation, J. Approx. Theory 74 (1993) 83-109; A. Durán, On orthogonal polynomials with respect to a positive definite matrix of measures, Canad. J. Math. 47 (1995) 88-112; A. Durán, W. van Assche, Orthogonal matrix polynomials and higher order recurrence relations, Linear Algebra Appl. 219 (1995) 261-280] but the existence of a differential operator having them as common eigenfunctions had not been considered. This correspondence goes only one way and most matrix valued situations do not arise in this fashion. We illustrate this general construction with a few examples. In the case of some families of scalar valued polynomials introduced in [F.A. Grünbaum, L. Haine, Bispectral Darboux transformations: An extension of the Krall polynomials, Int. Math. Res. Not. 8 (1997) 359-392] we take a first look at the algebra of all matrix differential operators that share these common eigenfunctions and uncover a number of phenomena that are new to the matrix valued case. 相似文献
15.
Yoonmee Ham Sang-Gu Lee Vu Quoc Phong 《Journal of Applied Mathematics and Computing》2011,36(1-2):233-239
A Toeplitz-like matrix has naturally occurred in the construction of iteration functions for finding zeroes of an analytic function. In this note, we study the properties of a Toeplitz-like matrix, and its relationship to the well known Toeplitz matrix involving normalized derivatives of an analytic function. 相似文献
16.
The paper is devoted to the construction of the matrix inverse of an infinite triangular matrix and to finding the connection coefficients between polynomial sequences and general combinatorial inversion formulas. 相似文献
17.
A spin model (for link invariants) is a square matrix W which satisfies certain axioms. For a spin model W, it is known that W T W ?1 is a permutation matrix, and its order is called the index of W. Jaeger and Nomura found spin models of index?2, by modifying the construction of symmetric spin models from Hadamard matrices. The aim of this paper is to give a construction of spin models of an arbitrary even index from any Hadamard matrix. In particular, we show that our spin models of indices a power of 2 are new. 相似文献
18.
The problem of cancelling a specified part of the zeros of a completely general rational matrix function by multiplication with an appropriate invertible rational matrix function is investigated from different standpoints. Firstly, the class of all factors that dislocate the zeros and feature minimal McMillan degree are derived. Further, necessary and sufficient existence conditions together with the construction of solutions are given when the factor fulfills additional assumptions like being J-unitary, or J-inner, either with respect to the imaginary axis or to the unit circle. The main technical tool are centered realizations that deliver a sufficiently general conceptual support to cope with rational matrix functions which may be polynomial, proper or improper, rank deficient, with arbitrary poles and zeros including at infinity. A particular attention is paid to the numerically-sound construction of solutions by employing at each stage unitary transformations, reliable numerical algorithms for eigenvalue assignment and efficient Lyapunov equation solvers. 相似文献
19.
Robert Brignall 《Journal of Combinatorial Theory, Series A》2012,119(1):99-116
We prove necessary and sufficient conditions on a family of (generalised) gridding matrices to determine when the corresponding permutation classes are partially well-ordered. One direction requires an application of Higman?s Theorem and relies on there being only finitely many simple permutations in the only non-monotone cell of each component of the matrix. The other direction is proved by a more general result that allows the construction of infinite antichains in any grid class of a matrix whose graph has a component containing two or more non-monotone-griddable cells. The construction uses a generalisation of pin sequences to grid classes, together with a number of symmetry operations on the rows and columns of a gridding. 相似文献
20.
We are generally concerned with the possible lists of multiplicities for the eigenvalues of a real symmetric matrix with a given graph. Many restrictions are known, but it is often problematic to construct a matrix with desired multiplicities, even if a matrix with such multiplicities exists. Here, we develop a technique for construction using the implicit function theorem in a certain way. We show that the technique works for a large variety of trees, give examples and determine all possible multiplicities for a large class of trees for which this was not previously known. 相似文献