Utilization of the method of linear matrix equations to solve a quasi-birth-death problem

1993 ◽  
Vol 30 (3) ◽  
pp. 639-649 ◽  
Author(s):  
Richard M. Feldman ◽  
Bryan L. Deuermeyer ◽  
Ciriaco Valdez-Flores
Keyword(s):  
Matrix Equation ◽  
Death Process ◽  
Linear Matrix ◽  
Boundary Values ◽  
Linear Matrix Equation ◽  
Machine Interference ◽  
Quadratic Matrix Equation ◽  
Recent Method ◽  
Linear Matrix Equations ◽  
Birth Death

The steady-state analysis of a quasi-birth-death process is possible by matrix geometric procedures in which the root to a quadratic matrix equation is found. A recent method that can be used for analyzing quasi-birth–death processes involves expanding the state space and using a linear matrix equation instead of the quadratic form. One of the difficulties of using the linear matrix equation approach regards the boundary conditions and obtaining the norming equation. In this paper, we present a method for calculating the boundary values and use the operator-machine interference problem as a vehicle to compare the two approaches for solving quasi-birth-death processes.

Utilization of the method of linear matrix equations to solve a quasi-birth-death problem

1993 ◽  
Vol 30 (03) ◽  
pp. 639-649
Author(s):  
Richard M. Feldman ◽  
Bryan L. Deuermeyer ◽  
Ciriaco Valdez-Flores
Keyword(s):  
Matrix Equation ◽  
Death Process ◽  
Linear Matrix ◽  
Boundary Values ◽  
Linear Matrix Equation ◽  
Machine Interference ◽  
Quadratic Matrix Equation ◽  
Recent Method ◽  
Linear Matrix Equations ◽  
Birth Death

The steady-state analysis of a quasi-birth-death process is possible by matrix geometric procedures in which the root to a quadratic matrix equation is found. A recent method that can be used for analyzing quasi-birth–death processes involves expanding the state space and using a linear matrix equation instead of the quadratic form. One of the difficulties of using the linear matrix equation approach regards the boundary conditions and obtaining the norming equation. In this paper, we present a method for calculating the boundary values and use the operator-machine interference problem as a vehicle to compare the two approaches for solving quasi-birth-death processes.

scholarly journals A Note on the⊤-Stein Matrix Equation

2013 ◽  
Vol 2013 ◽  
pp. 1-8 ◽  
Author(s):  
Chun-Yueh Chiang
Keyword(s):  
Matrix Equation ◽  
Sufficient Conditions ◽  
Linear Matrix ◽  
Comprehensive Treatment ◽  
Backward Error ◽  
Linear Matrix Equation ◽  
Perturbation Bounds ◽  
Necessary And Sufficient ◽  
The Relationship ◽  
Linear Matrix Equations

This note is concerned with the linear matrix equationX=AX⊤B + C, where the operator(·)⊤denotes the transpose (⊤) of a matrix. The first part of this paper sets forth the necessary and sufficient conditions for the unique solvability of the solutionX. The second part of this paper aims to provide a comprehensive treatment of the relationship between the theory of the generalized eigenvalue problem and the theory of the linear matrix equation. The final part of this paper starts with a brief review of numerical methods for solving the linear matrix equation. In relation to the computed methods, knowledge of the residual is discussed. An expression related to the backward error of an approximate solution is obtained; it shows that a small backward error implies a small residual. Just like the discussion of linear matrix equations, perturbation bounds for solving the linear matrix equation are also proposed in this work.Erratum to “A Note on the⊤-Stein Matrix Equation”

scholarly journals Solving Complex Fuzzy Linear Matrix Equations

2021 ◽  
Vol 2021 ◽  
pp. 1-11
Author(s):  
Yirong Sun ◽  
Junyang An ◽  
Xiaobin Guo
Keyword(s):  
Matrix Equation ◽  
Fuzzy Numbers ◽  
Linear Matrix ◽  
Matrix Equations ◽  
Linear Matrix Equation ◽  
Fuzzy Matrix ◽  
System Of Matrix Equations ◽  
Fuzzy Solution ◽  
Simplified Procedures ◽  
Linear Matrix Equations

In this paper, a kind of complex fuzzy linear matrix equation A X ˜ B = C ˜ , in which C ˜ is a complex fuzzy matrix and A and B are crisp matrices, is investigated by using a matrix method. The complex fuzzy matrix equation is extended into a crisp system of matrix equations by means of arithmetic operations of fuzzy numbers. Two brand new and simplified procedures for solving the original fuzzy equation are proposed and the correspondingly sufficient condition for strong fuzzy solution are analysed. Some examples are calculated in detail to illustrate our proposed method.

The anti-symmetric ortho-symmetric solution of a linear matrix equation and its optimal approximation

2008 ◽  
Vol 27 (1-2) ◽  
pp. 97-106 ◽  
Author(s):  
Lei Yu ◽  
Kaiyuan Zhang ◽  
Zhongke Shi
Keyword(s):  
Matrix Equation ◽  
Symmetric Solution ◽  
Optimal Approximation ◽  
Linear Matrix ◽  
Linear Matrix Equation

ZNN with Fuzzy Adaptive Activation Functions and Its Application to Time-Varying Linear Matrix Equation

2021 ◽  
pp. 1-1
Author(s):  
Jianhua Dai ◽  
Xing Yang ◽  
Lin Xiao ◽  
Lei Jia ◽  
Yiwei Li
Keyword(s):  
Matrix Equation ◽  
Linear Matrix ◽  
Time Varying ◽  
Activation Functions ◽  
Linear Matrix Equation ◽  
Fuzzy Adaptive

scholarly journals The Reflexive and Anti-Reflexive Solutions of a Linear Matrix Equation and Systems of Matrix Equations

2010 ◽  
Vol 40 (3) ◽  
pp. 825-848 ◽  
Author(s):  
Mehdi Dehghan ◽  
Masoud Hajarian
Keyword(s):  
Matrix Equation ◽  
Linear Matrix ◽  
Matrix Equations ◽  
Linear Matrix Equation
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