Solvability conditions and general solutions to some quaternion matrix equations
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DOI: 10.1002/mma.7696
Abstract: This paper studies some quaternion matrix equations. We use the equivalence canonical form to present some practical necessary and sufficient conditions for the existence of a solution to the system of quaternion matrix equations in… read more here.
Keywords: quaternion matrix; solvability conditions; matrix equations; conditions general ... See more keywords
A method for solving fuzzy matrix equations
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DOI: 10.1007/s00500-017-2680-x
Abstract: There are many reported studies, in which researchers tried to solve a system of fuzzy linear equations numerically. In this paper, a numerical method for solving fuzzy system $$A{\tilde{X}} B={\tilde{C}}$$AX~B=C~ of matrix equations is investigated.… read more here.
Keywords: method solving; solving fuzzy; matrix; matrix equations ... See more keywords
Low-rank updates and divide-and-conquer methods for quadratic matrix equations
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DOI: 10.1007/s11075-019-00776-w
Abstract: In this work, we consider two types of large-scale quadratic matrix equations: continuous-time algebraic Riccati equations, which play a central role in optimal and robust control, and unilateral quadratic matrix equations, which arise from stochastic… read more here.
Keywords: low rank; quadratic matrix; divide conquer; matrix equations ... See more keywords
Role extraction by matrix equations and generalized random walks
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DOI: 10.1007/s11075-025-02155-0
Abstract: The nodes in a network can be grouped into ’roles’ based on similar connection patterns. This is usually achieved by defining a pairwise node similarity matrix and then clustering rows and columns of this matrix.… read more here.
Keywords: random walks; role; role extraction; matrix equations ... See more keywords
Common solution to a pair of non-linear matrix equations via fixed point results
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DOI: 10.1007/s11784-019-0698-7
Abstract: In this paper, we propose an idea to derive some sufficient conditions for the existence and uniqueness of a positive definite common solution to a pair of non-linear matrix equations. To proceed with this, we… read more here.
Keywords: non linear; pair non; linear matrix; common solution ... See more keywords
The conjugate gradient methods for solving the generalized periodic Sylvester matrix equations
Sign Up to like & getrecommendations! Published in 2018 at "Journal of Applied Mathematics and Computing"
DOI: 10.1007/s12190-018-01220-3
Abstract: This work is devoted to designing two conjugate gradient methods for the least Frobenius norm solution of the generalized periodic Sylvester matrix equations. When the studied problem is consistent, the first conjugate gradient method can… read more here.
Keywords: generalized periodic; periodic sylvester; sylvester matrix; conjugate gradient ... See more keywords
Solving two generalized nonlinear matrix equations
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DOI: 10.1007/s12190-020-01448-y
Abstract: In this paper, we consider the numerical solutions of two generalized nonlinear matrix equations. Newton’s method is applied to compute one of the generalized nonlinear matrix equations and a generalized Stein equation is obtained, then… read more here.
Keywords: nonlinear matrix; solving two; generalized nonlinear; matrix equations ... See more keywords
Generalization of Roth's solvability criteria to systems of matrix equations
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DOI: 10.1016/j.laa.2017.04.011
Abstract: W.E. Roth (1952) proved that the matrix equation AX-XB=C has a solution if and only if the matrices View the MathML source and View the MathML source are similar. A. Dmytryshyn and B. Kagstrom (2015)… read more here.
Keywords: systems matrix; generalization roth; view mathml; mathml source ... See more keywords
A quadratically convergent algorithm based on matrix equations for inverse eigenvalue problems
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DOI: 10.1016/j.laa.2017.05.019
Abstract: Abstract We propose a quadratically convergent algorithm for inverse symmetric eigenvalue problems based on matrix equations. The basic idea is seen in a recent study by Ogita and Aishima, while they derive an efficient iterative… read more here.
Keywords: quadratically convergent; based matrix; inverse eigenvalue; eigenvalue problems ... See more keywords
An Inversion-Free Iterative Algorithm for Riccati Matrix Equations in Discrete-Time Markov Jump Systems
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DOI: 10.1109/tac.2022.3172266
Abstract: In this article, a novel iterative algorithm is proposed to obtain the positive definite solutions of the discrete coupled Riccati matrix equations. In the presented algorithm, there are no operations of matrix inversion in all… read more here.
Keywords: matrix; iterative algorithm; matrix equations; riccati matrix ... See more keywords
Comments on “An Inversion-Free Iterative Algorithm for Riccati Matrix Equations in Discrete-Time Markov Jump Systems”
Sign Up to like & getrecommendations! Published in 2024 at "IEEE Transactions on Automatic Control"
DOI: 10.1109/tac.2024.3417069
Abstract: Discrete coupled Riccati matrix equations, which play an important role in the analysis and design of discrete-time Markov jump systems of control theory, have been studied extensively. In Li et al. (2022), an iterative algorithm… read more here.
Keywords: time markov; discrete time; iterative algorithm; matrix equations ... See more keywords