«matrix equation»
۲۷٬۰۴۹ نتیجهOn the solving of matrix equation of Sylvester type
A solution of two problems related to the matrix equation of Sylvester type is given. In the first problem, the procedures for linear matrix inequalities are used to construct the solution of this equation. In the second problem, when a matrix is given which is not a solution of
On the solution of fuzzy Sylvester matrix equations without using Kronecker product and Vec-operation
It is known that using Kronecker product and Vec-operation for solving matrix equations under fuzzy uncertainty, make the dimension of the crisp transformed systems much higher than the dimension of the initial fuzzy matrix equation. In this paper, a new iterative approach is pro
iterative algorithm for the generalized $(p,q)$-reflexive solution of a quaternion matrix equation with $j$-conjugate of the unknowns
in the present paper, we propose an iterative algorithm for solving the generalized $(p,q)$-reflexive solution of the quaternion matrix equation $overset{u}{underset{l=1}{sum}}a_{l}xb_{l}+overset{v} {underset{s=1}{sum}}c_{s}widetilde{x}d_{s}=f$. by this iterative algorit
On the solving matrix equations by using the spectral representation
The purpose of this paper is to solve two types of Lyapunov equations and quadratic matrix equations by using the spectral representation. We focus on solving Lyapunov equations $AX+XA^*=C$ and $AX+XA^{T}=-bb^{T}$ for $A, X in mathbb{C}^{n times n}$ and $b in mathbb{C} ^{n t
Iterative algorithm for the generalized $(P,Q)$-reflexive solution of a quaternion matrix equation with $j$-conjugate of the unknowns
In the present paper, we propose an iterative algorithm for solving the generalized $(P,Q)$-reflexive solution of the quaternion matrix equation $\overset{u}{\underset{l=1}{\sum}}A_{l}XB_{l}+\overset{v} {\underset{s=1}{\sum}}C_{s}\widetilde{X}D_{s}=F$. By this iterative algorithm
theoretical results on the global gmres method for solving generalized sylvester matrix equations
the global generalized minimum residual (gl-gmres) method is examined for solving the generalized sylvester matrix equation [sumlimits_{i = 1}^q {a_i } xb_i = c.] some new theoretical results are elaborated for the proposed method by employing the schur complement. the
Theoretical results on the global GMRES method for solving generalized Sylvester matrix equations
The global generalized minimum residual (Gl-GMRES) method is examined for solving the generalized Sylvester matrix equation \[\sum\limits_{i = 1}^q {A_i } XB_i = C.\] Some new theoretical results are elaborated for the proposed method by employing the Schur complement. These resu
On the solution of parameterized Sylvester matrix equations
In this paper, parametric Sylvester matrix equations whose elements are linear functions of interval parameters are considered. In contrast to deterministic problems, when a system of equations is derived from a stochastic model, its coefficients may depend on some parameters and
the (r,s)-symmetric and (r,s)-skew symmetric solutions of the pair of matrix equations a1xb1 = c1 and a2xb2 = c2
let $rin textbf{c}^{mtimes m}$ and $sin textbf{c}^{ntimes n}$ be nontrivial involution matrices; i.e., $r=r^{-1}neq pm~i$ and $s=s^{-1}neq pm~i$. an $mtimes n$ complex matrix $a$ is said to be an $(r, s)$-symmetric ($(r, s)$-skew symmetric) matrix if $ras =a$ ($ ras =-a$). the $(
The (R,S)-symmetric and (R,S)-skew symmetric solutions of the pair of matrix equations A1XB1 = C1 and A2XB2 = C2
Let $Rin textbf{C}^{mtimes m}$ and $Sin textbf{C}^{ntimes n}$ be nontrivial involution matrices; i.e., $R=R^{-1}neq pm~I$ and $S=S^{-1}neq pm~I$. An $mtimes n$ complex matrix $A$ is said to be an $(R, S)$-symmetric ($(R, S)$-skew symmetric) matrix if $RAS =A$ ($ RAS =-A$). The $(