Positive definite solutions of the nonlinear matrix equation X+ AHX¯-1A= I
B Zhou, GB Cai, J Lam - Applied Mathematics and Computation, 2013 - Elsevier
This paper is concerned with the positive definite solutions to the nonlinear matrix equation
X+ AHX¯-1A= I where X is the unknown and A is a given complex matrix. By introducing and …
X+ AHX¯-1A= I where X is the unknown and A is a given complex matrix. By introducing and …
Positive operator based iterative algorithms for solving Lyapunov equations for Itô stochastic systems with Markovian jumps
ZY Li, B Zhou, J Lam, Y Wang - Applied Mathematics and Computation, 2011 - Elsevier
This paper studies the iterative solutions of Lyapunov matrix equations associated with Itô
stochastic systems having Markovian jump parameters. For the discrete-time case, when the …
stochastic systems having Markovian jump parameters. For the discrete-time case, when the …
Bauer's spectral factorization method for low order multiwavelet filter design
Para-Hermitian polynomial matrices obtained by matrix spectral factorization lead to
functions useful in control theory systems, basis functions in numerical methods or …
functions useful in control theory systems, basis functions in numerical methods or …
[PDF][PDF] Sensitivity of the matrix equation C+∑ k
In this paper, the sensitivity of the solution to the general type nonlinear matrix equation
C+∑ ki= 1 σiA∗ i Xpi Ai= 0, σi=±1 is studied, where k is a positive integer and pi, i= 1,... k are …
C+∑ ki= 1 σiA∗ i Xpi Ai= 0, σi=±1 is studied, where k is a positive integer and pi, i= 1,... k are …
The positive definite solution to a nonlinear matrix equation
J Meng, HM Kim - Linear and Multilinear Algebra, 2016 - Taylor & Francis
In this paper, we consider a nonlinear matrix equation, which has the form, where is a
positive integer, is an arbitrary complex matrix and is an Hermitian positive definite matrix. A …
positive integer, is an arbitrary complex matrix and is an Hermitian positive definite matrix. A …
Solvability Theory and Iteration Method for One Self‐Adjoint Polynomial Matrix Equation
Z Jia, M Zhao, M Wang, S Ling - Journal of Applied …, 2014 - Wiley Online Library
The solvability theory of an important self‐adjoint polynomial matrix equation is presented,
including the boundary of its Hermitian positive definite (HPD) solution and some sufficient …
including the boundary of its Hermitian positive definite (HPD) solution and some sufficient …
The extremal solution of the matrix equation Xs+ A∗ X-qA= I
M Wang, M Wei, S Hu - Applied Mathematics and Computation, 2013 - Elsevier
In this paper, the distribution of the positive definite solution of the nonlinear equation X s+
A∗ Xq A= I is deduced, the existence of the maximal solution and the minimal solution is …
A∗ Xq A= I is deduced, the existence of the maximal solution and the minimal solution is …
Hermitian Polynomial Matrix Equations and Applications
Z Jia, L Zhao, M Zhao - Matrix and Operator Equations and Applications, 2023 - Springer
In this chapter, we consider Hermitian polynomial matrix equations X s±∑ i= 1 ℓ δ i A i∗ X ti
A i= Q, which frequently arise from linear-quadratic control problems. The latest results of …
A i= Q, which frequently arise from linear-quadratic control problems. The latest results of …
Some inequalities for the nonlinear matrix equations
L Zhao - Mathematical Inequalities & Applications, 2013 - files.ele-math.com
The nonlinear matrix equations X±A∗ X− 1A= Q have many applications in control theory,
dynamic programming and statistics. In the present work, by using some related matrix …
dynamic programming and statistics. In the present work, by using some related matrix …
Positive Definite Solutions of the Nonlinear Matrix Equation
B Zhou, GB Cai, J Lam - arXiv preprint arXiv:1211.1872, 2012 - arxiv.org
This paper is concerned with the positive definite solutions to the matrix equation $ X+
A^{\mathrm {H}}\bar {X}^{-1} A= I $ where $ X $ is the unknown and $ A $ is a given complex …
A^{\mathrm {H}}\bar {X}^{-1} A= I $ where $ X $ is the unknown and $ A $ is a given complex …