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An iteration method for the symmetric solutions and the optimal approximation solution of the matrix equation AXB=C

An iteration method is constructed to solve the linear matrix equation AXB=C over symmetric X. By this iteration method, the solvability of the equation AXB=C over symmetric X can be determined… Expand

The reflexive and anti-reflexive solutions of the matrix equation AX = B

Abstract An n × n complex matrix P is said to be a generalized reflection matrix if P H = P and P 2 = I . An n × n complex matrix A is said to be a reflexive (or anti-reflexive) matrix with respect… Expand

Two inverse eigenvalue problems for a special kind of matrices

In this paper, a special kind of matrices which are symmetric, all elements are equal to zero except for the first row, the first column and the diagonal elements, and the elements of the first row… Expand

An iterative method for symmetric solutions and optimal approximation solution of the system of matrix equations A1XB1 = C1, A2XB2 = C2

Abstract The symmetric solutions of the system of matrix equations A1XB1 = C1, A2XB2 = C2 are too difficult to be obtained by applying matrices decomposition. In this paper, an iterative method is… Expand

The skew-symmetric orthogonal solutions of the matrix equation AX=B☆

- Chunjun Meng, Xi-Yan Hu, Lei Zhang
- Mathematics
- 1 June 2005

Abstract An n × n real matrix X is said to be a skew-symmetric orthogonal matrix if XT = −X and XTX = I. Using the special form of the C–S decomposition of an orthogonal matrix with skew-symmetric k… Expand

The bisymmetric solutions of the matrix equation A1X1B1+A2X2B2+⋯+AlXlBl=C and its optimal approximation☆

- Zhuo-hua Peng, Xi-Yan Hu, L. Zhang
- Mathematics
- 15 October 2007

Abstract A matrix A = ( a ij ) ∈ R n × n is said to be bisymmetric matrix if a ij = a ji = a n + 1 - j , n + 1 - i for all 1 ⩽ i , j ⩽ n . In this paper, an iterative method is constructed to find… Expand

The generalized anti-reflexive solutions for a class of matrix equations (BX = C, XD = E)

- Fan-Liang Li, Xi-Yan Hu, L. Zhang
- Mathematics
- 2008

In this paper, the generalized anti-reflexive solution for matrix equations (BX = C, XD = E), which arise in left and right inverse eigenpairs problem, is considered. With the special properties of… Expand

THE NEAREST BISYMMETRIC SOLUTIONS OF LINEAR MATRIX EQUATIONS ∗1)

- Zhen-Yun Peng, Xi-Yan Hu, L. Zhang
- Mathematics
- 2004

The necessary and sufficient conditions for the existence of and the expressions for the bisymmetric solutions of the matrix equations (I) A1X1B1 +A2X2B2 +···+AkXkBk = D, (II) A1XB1 + A2XB2 + ···+… Expand

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On the construction of a Jacobi matrix from its mixed-type eigenpairs

In this paper, an inverse eigenvalue problem of constructing a Jacobi matrix from its mixedtype eigenpairs is considered. The necessary and sufficient conditions for the existence and uniqueness of… Expand

New symmetry preserving method for optimal correction of damping and stiffness matrices using measured modes

Measured and analytical data are unlikely to be equal due to measured noise, model inadequacies, structural damage, etc. It is necessary to update the physical parameters of analytical models for… Expand