Solutions of the Lyapunov matrix equationBX - XA = C

The main purpose of this correspondence is to establish an expression for the solution of the Lyapunov matrix equation in terms of the principal indempotents and nilpotents of the coefficient matrices. The coefficient matrices are not necessarily of the same size and may have common characteristic roots and have elements belonging to the field of complex numbers.     

On the fuzzy difference equation xn+1 = A+B/xn

 In this paper we study the existence the oscillatory behavior the boundedness and the asymptotic behavior of the positive solutions of the fuzzy equation x _n+1 =A+B/x _n ,n=0,1,… where x _n is a sequence of fuzzy numbers, A, B are fuzzy numbers.     

Numerical solution of the matrix equation AX + XAT+ B = 0

A recursive algorithm is shown to solve the above equation accurately for large (n leq 146), lightly damped (zeta geq 10^{-3}) systems. About2.5n^{2}storage locations are required, and about2.5n^{3}multiplications are performed per recursion, ten recursions being typical.     

The general problem of pole assignment: A polynomial equation approach

The problem of modifying the invariant polynomials of a linear system by dynamical output feedback is considered. A new necessary condition which the invariant polynomials must satisfy is derived. The sufficiency condition of Rosenbrock and Hayton is proved in an alternative way. The proof is based on polynomial matrix equations and provides a simple construction of the feedback which affects the desirable change.     

An algorithm for solving the matrix equation X = FXF T + S

A now algorithm for solving the matrix equation X = FXF ^T + S, which is important in the control system design, is presented in this paper. The algorithm is based on the QR algorithm for finding the eigenvalues of a matrix and works efficiently for large dimensional problems. A simple example is given to illustrate the algorithm. The method is also applicable to other types of equations such as the Lyapunov equation A ^T X + XA + B = 0.     

Solving the generalized Sylvester matrix equation AV +BW = VF via Kronecker map

This note considers the solution to the generalized Sylvester matrix equation AV ＋ BW = VF with F being an arbitrary matrix, where V and W are the matrices to be determined. With the help of the Kronecker map, an explicit parametric solution to this matrix equation is established. The proposed solution possesses a very simple and neat form, and allows the matrix F to be undetermined.     

通过复S出入形求解线性方程AX+XB=-C*

控制系统设计中经常要遇到求解线性方程AX+XB=—C (1)的需求,因而在各种CADCS软件包中都包含求解这类方程的功能,本文介绍的方法用于矩阵设计工具MXTOOL中,其特点是适用范围广,数值稳定性高。     

The reflexive solutions of the matrix equation AX B = C

In this paper, we study the existence of a reflexive, with respect to the generalized reflection matrix P, solution of the matrix equation AX B = C. For the special case when B = I, we get the result of Peng and Hu [1].     

Least-squares problem for the quaternion matrix equation AXB+CYD=E over different constrained matrices

For any A=A ₁+A ₂ j∈Q ^n×n and η∈<texlscub>i, j, k</texlscub>, denote A ^{η H} =?η A ^H η. If A ^{η H} =A, A is called an $\eta$-Hermitian matrix. If A ^{η H} =?A, A is called an η-anti-Hermitian matrix. Denote η-Hermitian matrices and η-anti-Hermitian matrices by η HQ ^n×n and η AQ ^n×n , respectively.

By using the complex representation of quaternion matrices, the Moore–Penrose generalized inverse and the Kronecker product of matrices, we derive the expressions of the least-squares solution with the least norm for the quaternion matrix equation AXB+CYD=E over X∈η HQ ^n×n and Y∈η AQ ^n×n .     

PostgreSQL数据库XA协议的设计和实现

ＸＡ协议是分布事务处理中子事务与全局事务间通讯的接口规范,ＰｏｓｔｇｒｅＳＱＬ是一种集中式的数据库管理系统,尚未实现对ＸＡ协议的支持。在对数据库事务管理和存储管理分析的基础上,提出了ＰｓｔｇｒｅＳＱＬ上ＸＡ协议的实现方法,并对事务预交后的恢复提出一种独特的解决方案。     

Solution to the second-order Sylvester matrix equation MVF/sup 2/+DVF+KV=BW

This note provides a complete general parametric solution (V,W) to the generalized second-order Sylvester matrix equation MVF/sup 2/+DVF+KV=BW, with F being an arbitrary square matrix. The primary feature of this solution is that the matrix F does not need to be in any canonical form, or may be even unknown a priori. The results provide great convenience to the computation and analysis of the solutions to this class of equations, and can perform important functions in many analysis and design problems involving second-order dynamical systems.     

The vmf90 program for the numerical resolution of the Vlasov equation for mean-field systems

The numerical resolution of the Vlasov equation provides complementary information with respect to analytical studies and forms an important research tool in domains such as plasma physics. The study of mean-field models for systems with long-range interactions is another field in which the Vlasov equation plays an important role. We present the vmf90 program that performs numerical simulations of the Vlasov equation for this class of mean-field models with the semi-Lagrangian method.     

Exponential-fitting methods for the numerical integration of the fourth-order differential equation y IV +f·y=g

A class of multistep methods is derived from the Chebyshevian multistep theory of Lyche for the numerical integration of the fourth-order differential equation of the formy ^IV +f·y=g. The new methods are significantly more accurate than the classical methods iff(x) is a nearly constant function.     

Further results on controllability and the linear equation Ax = b

The linear equation Ax = b, with A an n × n matrix and b an n × l matrix over a unique factorization domain R, is related to the controllability submodule U of the pair (A, b). It is shown that the above equation has a solution lying in V if, and only if, A is unimodular as an operator on U. An example is given of a matrix which is unimodular as an operator on the controllability submodule, but not as an operator on Rⁿ and sparseness of this occurrence is discussed.     

Solution of the matrix equation AX−XB=C

In this paper a finite algebraic formula for the solution of the matrix equationAX?XB=C is derived. Based on it, a new direct algorithm is given.     

Finite iterative algorithms for the generalized Sylvester-conjugate matrix equation {AX+BY=E\overline{X}F+S}

This paper investigates the generalized Sylvester-conjugate matrix equation, which includes the normal Sylvester-conjugate, Kalman–Yakubovich-conjugate and generalized Sylvester matrix equations as its special cases. An iterative algorithm is presented for solving such a kind of matrix equations. This iterative method can give an exact solution within finite iteration steps for any initial values in the absence of round-off errors. Another feature of the proposed algorithm is that it is implemented by original coefficient matrices. By specifying the proposed algorithm, iterative algorithms for some special matrix equations are also developed. Two numerical examples are given to illustrate the effectiveness of the proposed methods.