On the Sylvester-like matrix equation <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si0001.gif" overflow="scroll"><mml:mi mathvariant="italic">AX</mml:mi><mml:mo>+</mml:mo><mml:mi>f</mml:mi><mml:mo>(</mml:mo><mml:mi>X</mml:mi><mml:mo>)</mml:mo><mml:mi>B</mml:mi><mml:mo>=</mml:mo><mml:mi>C</mml:mi></mml:math>

Chiang, Chun-Yueh

doi:10.1016/j.jfranklin.2015.03.024

Journal of the Franklin Institute

2016

DOI: 10.1016/j.jfranklin.2015.03.024

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On the Sylvester-like matrix equation AX+f(X)B=C

Chun-Yueh Chiang

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Cited by 13 publications

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“…[22] proposes an effective algorithm for the periodic discretetime Riccati equation arising from a linear periodic time-varying system (A k , B k ), which is particularly efficient when A k is time-invariant and B k is periodic, and has special property associated with the problem of spacecraft attitude control using magnetic torques. [4] discuss the solvability of the Sylvester-like matrix equation AX + f (X)B = C through an auxiliary standard (or generalized) Sylvester matrix equation. [10] proposes a gradient based iterative method to find the solutions of the general Sylvester discrete-time periodic matrix equations, which is proven that the proposed iterative method can obtain the solutions of the periodic matrix equations for any initial matrices.…”

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confidence: 99%

An iterative algorithm for periodic sylvester matrix equations

Lv¹,

Zhang²,

Zhang³

et al. 2018

Journal of Industrial &Amp; Management Optimization

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The problem of solving periodic Sylvester matrix equations is discussed in this paper. A new kind of iterative algorithm is proposed for constructing the least square solution for the equations. The basic idea is to develop the solution matrices in the least square sense. Two numerical examples are presented to illustrate the convergence and performance of the iterative method. 2010 Mathematics Subject Classification. 15A24.

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confidence: 99%

An iterative algorithm for periodic sylvester matrix equations

Lv¹,

Zhang²,

Zhang³

et al. 2018

Journal of Industrial &Amp; Management Optimization

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A Numerical Approach To Generalized Periodic Sylvester Matrix Equation

Zhang

2018

Asian Journal of Control

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The paper is dedicated to solving the generalized periodic discrete‐time Sylvester matrix equation, which is frequently encountered in control theory and applied mathematics. An iterative algorithm for this equation is presented. The proposed method is developed from a point of least squares method. The rationality of the method is testified by theoretical analysis. The presented approach is numerically reliable and requires less computation. Two numerical examples illustrate the effectiveness of the raised results.

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Reflexive periodic solutions of general periodic matrix equations

Hajarian

2019

Math Methods in App Sciences

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Analysis and design of linear periodic control systems are closely related to the periodic matrix equations. The objective of this paper is to provide four new iterative methods based on the conjugate gradient normal equation error (CGNE), conjugate gradient normal equation residual (CGNR), and least‐squares QR factorization (LSQR) algorithms to find the reflexive periodic solutions (X1,Y1,X2,Y2,…,Xσ,Yσ) of the general periodic matrix equations ∑s=0σ−1Ai,sXi+sBi,s+∑t=0σ−1Ci,tYi+tDi,t=Ni, for i = 1,2,…,σ. The iterative methods are guaranteed to converge in a finite number of steps in the absence of round‐off errors. Finally, some numerical results are performed to illustrate the efficiency and feasibility of new methods.

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On the Sylvester-like matrix equation AX+f(X)B=C

Cited by 13 publications

References 18 publications

An iterative algorithm for periodic sylvester matrix equations

An iterative algorithm for periodic sylvester matrix equations

A Numerical Approach To Generalized Periodic Sylvester Matrix Equation

Reflexive periodic solutions of general periodic matrix equations

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