Di Zhao

Least squares solutions of the matrix equation AXB+CYD=E with the least norm for symmetric arrowhead matrices

In this paper, the least squares solution of the matrix equation AXB+CYD=E for symmetric arrowhead matrices with the least norm is discussed. By using Moore-Penrose inverse and the Kronecker product, the general expression of the solution to this problem is derived. A corresponding numerical algorithm and an example are also given.

On the spectral radius of a nonnegative centrosymmetric matrix

Abstract In this paper, we discuss the spectral radius of nonnegative centrosymmetric matrices. By using the centrosymmetric structure, we establish some estimations of the spectral radius.

On the computation of inverses and determinants of a kind of special matrices

Abstract In this paper, the inverse and determinant of a special kind of centrosymmetric matrices are investigated. Based on the partition property of a matrix with centrosymmetric structure and algorithms for the inverse and determinant proposed in Chen and Yu (2011), a computation algorithm for the inverse and determinant of a centrosymmetric matrix is finally developed.

An extension of the Golden-Thompson theorem

In this paper, we shall prove |treA+B|≤tr(|eA||eB|) for normal matrices A, B. In particular, treA+B≤tr(eAeB) if A, B are Hermitian matrices, yielding the Golden-Thompson inequality.MSC:15A16, 47A63, 15A45.

Notes on Greub-Rheinboldt inequalities

In this paper, we focus on matrix Greub-Rheinboldt inequalities for commutative positive definite Hermitian matrix pairs. Some improvements, which yield sharpened bounds compared with existing results, are presented.

An improved empirical mode decomposition method based on the cubic trigonometric B-spline interpolation algorithm

Empirical mode decomposition (EMD) is a new method presented recently for analyzing nonlinear and non-stationary signals. Its basic idea is to decompose the signal into a series of complete orthogonal intrinsic mode functions (IMFs) based on the local characteristics of the signal in time domain. The key step of EMD is to use the cubic spline interpolation to connect the maximum and minimum values of the signals into upper and lower envelopes respectively, and then calculate the mean values of upper and lower envelopes. Based on the cubic trigonometric B-spline interpolation algorithm, a new improved method for EMD is proposed named CTB-EMD in this paper. In this method, the interpolation curve is more flexible because of the adjustability of shape of the cubic trigonometric B-splines curve. Thus, the overshoot and undershoot problems in the cubic spline interpolation curve can be avoided, and then the decomposition of the signal is more accurate and effect. Through numerical experiments, we compare the effect of this method with other methods on decomposing simulation signals and real signals. Experimental results show that this method can decompose signals more effectively and accurately.

A Numerical Algorithm on the Computation of the Stationary Distribution of a Discrete Time Homogenous Finite Markov Chain

The transition matrix, which characterizes a discrete time homogeneous Markov chain, is a stochastic matrix. A stochastic matrix is a special nonnegative matrix with each row summing up to 1. In this paper, we focus on the computation of the stationary distribution of a transition matrix from the viewpoint of the Perron vector of a nonnegative matrix, based on which an algorithm for the stationary distribution is proposed. The algorithm can also be used to compute the Perron root and the corresponding Perron vector of any nonnegative irreducible matrix. Furthermore, a numerical example is given to demonstrate the validity of the algorithm.

A Schwarz–Pick lemma for the modulus of holomorphic mappings from to

Abstract In this paper, we consider a holomorphic mapping f between p-balls from to , where with a positive integer p satisfying . It is proved that for such f, We also discuss the extreme case when p is even. This extends some related results on Schwarz–Pick lemma.

Peak function and support surface of a general Kohn–Nirenberg domain in ℂ n

In this article, we consider a general modification of the Kohn–Nirenberg domain in ℂ n , namely, . In particular, we study the existence of support surface and the regularity of peak function at the point 0∈∂Ω k .

A note on the Frobenius conditional number with positive definite matrices

In this article, we focus on the lower bounds of the Frobenius condition number. Using the generalized Schwarz inequality, we present some lower bounds for the Frobenius condition number of a positive definite matrix depending on its trace, determinant, and Frobenius norm. Also, we give some results on a kind of matrices with special structure, the positive definite matrices with centrosymmetric structure.