共查询到20条相似文献,搜索用时 31 毫秒
1.
The matrix equation AX = B with PX = XP and XH = sX constraints is considered, where P is a given Hermitian involutory matrix and s = ±1. By an eigenvalue decomposition of P, we equivalently transform the constrained problem to two well-known constrained problems and represent the solutions in terms of the eigenvectors of P. Using Moore-Penrose generalized inverses of the products generated by matrices A, B and P, the involved eigenvectors can be released and eigenvector-free formulas of the general solutions are presented. Similar strategy is applied to the equations AX = B, XC = D with the same constraints. 相似文献
2.
Yongxin Yuan 《Applied mathematics and computation》2010,216(10):3120-3125
The least-squares solution and the least-squares symmetric solution with the minimum-norm of the matrix equations AX = B and XC = D are considered in this paper. By the matrix differentiation and the spectral decomposition of matrices, an explicit representation of such solution is given. 相似文献
3.
Yabo Chen 《Applied mathematics and computation》2010,217(1):230-236
A new matrix based iterative method is presented to compute common symmetric solution or common symmetric least-squares solution of the pair of matrix equations AXB = E and CXD = F. By this iterative method, for any initial matrix X0, a solution X∗ can be obtained within finite iteration steps if exact arithmetic was used, and the solution X∗ with the minimum Frobenius norm can be obtained by choosing a special kind of initial matrix. In addition, the unique nearest common symmetric solution or common symmetric least-squares solution to given matrix in Frobenius norm can be obtained by first finding the minimum Frobenius norm common symmetric solution or common symmetric least-squares solution of the new pair of matrix equations. The given numerical examples show that the matrix based iterative method proposed in this paper has faster convergence than the iterative methods proposed in [1] and [2] to solve the same problems. 相似文献
4.
In this paper, the nonlinear matrix equation X + A∗XqA = Q (q > 0) is investigated. Some necessary and sufficient conditions for existence of Hermitian positive definite solutions of the nonlinear matrix equations are derived. An effective iterative method to obtain the positive definite solution is presented. Some numerical results are given to illustrate the effectiveness of the iterative methods. 相似文献
5.
Jing Cai 《Applied mathematics and computation》2010,217(1):117-4466
Nonlinear matrix equation Xs + A∗X−tA = Q, where A, Q are n × n complex matrices with Q Hermitian positive definite, has widely applied background. In this paper, we consider the Hermitian positive definite solutions of this matrix equation with two cases: s ? 1, 0 < t ? 1 and 0 < s ? 1, t ? 1. We derive necessary conditions and sufficient conditions for the existence of Hermitian positive definite solutions for the matrix equation and obtain some properties of the solutions. We also propose iterative methods for obtaining the extremal Hermitian positive definite solution of the matrix equation. Finally, we give some numerical examples to show the efficiency of the proposed iterative methods. 相似文献
6.
Fengxia Zhang Ying LiWenbin Guo Jianli Zhao 《Applied mathematics and computation》2011,217(24):10049-10057
In this article we give some formulas for the maximal and minimal ranks of the submatrices in a least squares solution X to AXB = C. From these formulas, we derive necessary and sufficient conditions for the submatrices to be zero and other special forms, respectively. Finally, some Hermitian properties for least squares solution to matrix equation AXB = C are derived. 相似文献
7.
Alegra Daji? 《Linear algebra and its applications》2008,429(7):1779-1809
This paper reviews the equations ax = c and xb = d from a new perspective by studying them in the setting of associative rings with or without involution. Results for rectangular matrices and operators between different Banach and Hilbert spaces are obtained by embedding the ‘rectangles’ into rings of square matrices or rings of operators acting on the same space. Necessary and sufficient conditions using generalized inverses are given for the existence of the hermitian, skew-hermitian, reflexive, antireflexive, positive and real-positive solutions, and the general solutions are described in terms of the original elements or operators. New results are obtained, and many results existing in the literature are recovered and corrected. 相似文献
8.
Two perturbation estimates for maximal positive definite solutions of equations X + A*X−1A = Q and X − A*X−1A = Q are considered. These estimates are proved in [Hasanov et al., Improved perturbation Estimates for the Matrix Equations X ± A*X−1A = Q, Linear Algebra Appl. 379 (2004) 113-135]. We derive new perturbation estimates under weaker restrictions on coefficient matrices of the equations. The theoretical results are illustrated by numerical examples. 相似文献
9.
Houria Triki 《Applied mathematics and computation》2010,217(4):1733-9479
We consider the nonlinear dispersive K(m,n) equation with the generalized evolution term and derive analytical expressions for some conserved quantities. By using a solitary wave ansatz in the form of sechp function, we obtain exact bright soliton solutions for (2 + 1)-dimensional and (3 + 1)-dimensional K(m,n) equations with the generalized evolution terms. The results are then generalized to multi-dimensional K(m,n) equations in the presence of the generalized evolution term. An extended form of the K(m,n) equation with perturbation term is investigated. Exact bright soliton solution for the proposed K(m,n) equation having higher-order nonlinear term is determined. The physical parameters in the soliton solutions are obtained as function of the dependent model coefficients. 相似文献
10.
In this paper we study the class of square matrices A such that AA† − A†A is nonsingular, where A† stands for the Moore-Penrose inverse of A. Among several characterizations we prove that for a matrix A of order n, the difference AA† − A†A is nonsingular if and only if R(A)⊕R(A∗)=Cn,1, where R(·) denotes the range space. Also we study matrices A such that R(A)⊥=R(A∗). 相似文献
11.
Let M denote a 2 × 2 block complex matrix , where A and D are square matrices, not necessarily with the same orders. In this paper explicit representations for the Drazin inverse of M are presented under the condition that BDiC = 0 for i = 0, 1, … , n − 1, where n is the order of D. 相似文献
12.
13.
Xinyun Zhu 《Linear algebra and its applications》2008,428(4):919-929
We show that under certain conditions, the N = 1 types A and D quivers are of finite representation type. 相似文献
14.
The extremal ranks of matrix expression of A − BXC with respect to XH = X have been discussed by applying the quotient singular value decomposition Q-SVD and some rank equalities of matrices in this paper. 相似文献
15.
Toma? Kosem 《Linear algebra and its applications》2006,418(1):153-160
The conjecture posed by Aujla and Silva [J.S. Aujla, F.C. Silva, Weak majorization inequalities and convex functions, Linear Algebra Appl. 369 (2003) 217-233] is proved. It is shown that for any m-tuple of positive-semidefinite n × n complex matrices Aj and for any non-negative convex function f on [0, ∞) with f(0) = 0 the inequality ?f(A1) + f(A2) + ? + f(Am)? ? ? f(A1 + A2 + ? + Am)? holds for any unitarily invariant norm ? · ?. It is also proved that ?f(A1) + f(A2) + ? + f(Am)? ? f(?A1 + A2 + ? + Am?), where f is a non-negative concave function on [0, ∞) and ? · ? is normalized. 相似文献
16.
A matrix A∈Rn×n is called a bisymmetric matrix if its elements ai,j satisfy the properties ai,j=aj,i and ai,j=an-j+1,n-i+1 for 1?i,j?n. This paper considers least squares solutions to the matrix equation AX=B for A under a central principal submatrix constraint and the optimal approximation. A central principal submatrix is a submatrix obtained by deleting the same number of rows and columns in edges of a given matrix. We first discuss the specified structure of bisymmetric matrices and their central principal submatrices. Then we give some necessary and sufficient conditions for the solvability of the least squares problem, and derive the general representation of the solutions. Moreover, we also obtain the expression of the solution to the corresponding optimal approximation problem. 相似文献
17.
Tetsutaro Shibata 《Journal of Mathematical Analysis and Applications》2002,267(2):576-598
We consider the nonlinear eigenvalue problem on an interval−u″(t)+g(u(t))=λsinu(t),u(t)>0,t∈I:=(−T,T),u(±T)=0,where λ > 0 is a parameter and T > 0 is a constant. It is known that if λ ? 1, then the corresponding solution has boundary layers. In this paper, we characterize λ by the boundary layers of the solution when λ ? 1 from a variational point of view. To this end, we parameterize a solution pair (λ, u) by a new parameter 0 < ?< T, which characterizes the boundary layers of the solution, and establish precise asymptotic formulas for λ(?) with exact second term as ? → 0. It turns out that the second term is a constant which is explicitly determined by the nonlinearity g. 相似文献
18.
Albert Compta 《Linear algebra and its applications》2007,421(1):45-52
Given an observable pair of matrices (C, A) we consider the manifold of (C, A)-invariant subspaces having a fixed Brunovsky-Kronecker structure. Using Arnold techniques we obtain the explicit form of a miniversal deformation of a marked (C, A)-invariant subspace with respect to the usual equivalence relation. As an application, we obtain the dimension of the orbit and we characterize the structurally stable subspaces (those with open orbit). 相似文献
19.
For the pair of matrix equations AX = C, XB = D this paper gives common solutions of minimum possible rank and also other feasible specified ranks. 相似文献
20.
This paper develops a gradient based and a least squares based iterative algorithms for solving matrix equation AXB + CXTD = F. The basic idea is to decompose the matrix equation (system) under consideration into two subsystems by applying the hierarchical identification principle and to derive the iterative algorithms by extending the iterative methods for solving Ax = b and AXB = F. The analysis shows that when the matrix equation has a unique solution (under the sense of least squares), the iterative solution converges to the exact solution for any initial values. A numerical example verifies the proposed theorems. 相似文献