An upper bound on algebraic connectivity of graphs with many cutpoints.
Analysis of straightening formula.
Analytic aspects of the circulant Hadamard conjecture
We investigate the problem of counting the real or complex Hadamard matrices which are circulant, by using analytic methods. Our main observation is the fact that for the quantity satisfies , with equality if and only if is the eigenvalue vector of a rescaled circulant complex Hadamard matrix. This suggests three analytic problems, namely: (1) the brute-force minimization of , (2) the study of the critical points of , and (3) the computation of the moments of . We explore here these questions,...
Approximation of fractional positive stable continuous-time linear systems by fractional positive stable discrete-time systems
Fractional positive asymptotically stable continuous-time linear systems are approximated by fractional positive asymptotically stable discrete-time systems using a linear Padé-type approximation. It is shown that the approximation preserves the positivity and asymptotic stability of the systems. An optional system approximation is also discussed.
Asymptotic enumeration of dense 0-1 matrices with equal row sums and equal column sums.
Asymptotics for weakly dependent errors-in-variables
Linear relations, containing measurement errors in input and output data, are taken into account in this paper. Parameters of these so-called errors-in-variables (EIV) models can be estimated by minimizing the total least squares (TLS) of the input-output disturbances. Such an estimate is highly non-linear. Moreover in some realistic situations, the errors cannot be considered as independent by nature. Weakly dependent (- and -mixing) disturbances, which are not necessarily stationary nor identically...
Asymptotics of the partition function of a random matrix model
We prove a number of results concerning the large asymptotics of the free energy of a random matrix model with a polynomial potential. Our approach is based on a deformation of potential and on the use of the underlying integrable structures of the matrix model. The main results include the existence of a full asymptotic expansion in even powers of of the recurrence coefficients of the related orthogonal polynomials for a one-cut regular potential and the double scaling asymptotics of the free...
Base tensorielle des matrices de Hankel (ou de Toeplitz) Applications.
Binary Moore-Penrose inverses of set inclusion incidence matrices.
Binomial matrices
Block distance matrices.
Block Factorization of Hankel Matrices and Euclidean Algorithm
It is shown that a real Hankel matrix admits an approximate block diagonalization in which the successive transformation matrices are upper triangular Toeplitz matrices. The structure of this factorization was first fully discussed in [1]. This approach is extended to obtain the quotients and the remainders appearing in the Euclidean algorithm applied to two polynomials u(x) and v(x) of degree n and m, respectively, whith m < ...
Block matrix approximation via entropy loss function
The aim of the paper is to present a procedure for the approximation of a symmetric positive definite matrix by symmetric block partitioned matrices with structured off-diagonal blocks. The entropy loss function is chosen as approximation criterion. This procedure is applied in a simulation study of the statistical problem of covariance structure identification.
Bounds and inequalities for the Perron root of a nonnegative matrix. III: Bounds dependent on simple paths and circuits.
Bounds for Exponents of Doubly Stochastic Primitive Matrices.
Bounds for graph expansions via elasticity.
Bounds for the singular values of a matrix involving its sparsity pattern.
Bounds for the spectral radius of block -matrices.
Bounds for the spectral radius of nonnegative matrices
Bounds for the Z-eigenpair of general nonnegative tensors
In this paper, we consider the Z-eigenpair of a tensor. A lower bound and an upper bound for the Z-spectral radius of a weakly symmetric nonnegative irreducible tensor are presented. Furthermore, upper bounds of Z-spectral radius of nonnegative tensors and general tensors are given. The proposed bounds improve some existing ones. Numerical examples are reported to show the effectiveness of the proposed bounds.