Matrix equationsNumerical solutionsStein equationsThis paper studies the solvability, existence of unique solution, closed-form solution and numerical solution of matrix equation X=Af(X) B+C with f(X)=XT, f(X)=X and f(X)=XH, where X is the unknown. It is proven that the solvability of...
Eventually I hit the point where you have an equation relating to the undefined variables m11 m12 m21 m22 and I gave up trying to fix at that point. You do not define A1, A2, B1, B2 before they are used, and you overwrite some of them after they are used which is confusing. You...
into(9),andcomparethecoefficientsofthetwosidesoftheobtainedequations,we have Ao-I7oB=-C. AX~-Xo-I11B+I7o=0. AX2-X1- Y2B+Y1=0. ... (11) AXI-XI-1 -glB+Yl-1=0. -X~+Yz=O. SolutionoftheMatrixEquationAX-XB=C 353 Respectively,multiplying the 1st, 2nd ... ,/-th terms of ...
5) matrix equation over a skew field 体上的矩阵方程 6) Matrix Equation 矩阵方程 1. Iterative solution to a class of matrix equation; 一类矩阵方程的迭代解法 2. The least-square solution of the matrix equation A~TXA=D in anti-symmetric and persymmetric matrix; ...
This paper is concerned with the solution of a matrix Riccati equation encountered in quadratic minimization problems of optimal and filtering control theory. The classical perturbation method is employed to obtain the solution in the form of a series which is shown to be convergent in transient as...
摘要: A new way of solving the matrix equation + = is presented in the form (Vec ) = ().(Vec ). The solution makes use of the properties of the Kronecker products and is particularly suitable for finding in terms of a fixed set of and and a varying ....
The main is to develop a method to solve an arbitrary fuzzy matrix equation system by using the embedding approach. Considering the existing solution to fuzzy matrix equation system is done. To illustrate the proposed model a numerical example is given,
The purpose of this paper is to study the existence and uniqueness of a positive definite solution to the nonlinear matrix equation X = Q − A∗X −1A + B∗X −1B, which is a special stochastic rational Riccati equation arising in stochastic control theory. Methods Ou...
This paper studies the nonnegative definite solution of the matrix equation AXA *=B over quaternion field. The following problems are solved: (1) The necessary and sufficient condition for the existence of the nonnegative definite solution to the matrix equation AXA *=B ; (2) If the equation...
positive definite solutionIn this note, we argue that Theorem 2.2 and its proof in Duan XF, et al. is seriously flawed and prove a new result based on Brouwer’s fixed-point theorem.Keywords: nonlinear matrix equation, stochastic control, positive definite solution, AMS Subject ...