在這本書中，主要研究了一些線性矩陣方程的有限迭代算法、MCGLS迭代算法及解析算法。本書提出線性矩陣方程的兩類算法(有限迭代算法和MCGLS迭代算法)并推廣到耦合算子矩陣方程上，同時(shí)把線性矩陣方程的一般迭代解推廣到約束解，這兩類算法的各章節(jié)之間密切相關(guān)并層層遞進(jìn)。最后，本書給出了幾類線性矩陣方程的解析算法，推廣了國外專家的已有結(jié)論。
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Contents
About the Author
Preface
Notations
CHAPTER 1 Introduction 1
1.1 The First Part: Finite Iterative Algorithm to Linear Matrix Equation 1
1.2 The Second Part: MCGLS Iterative Algorithm to Linear Matrix Equation 3
1.3 The Third Part: Explicit Solutions to Linear Matrix Equation 5
CHAPTER 2 Finite Iterative Algorithm to Coupled Transpose Matrix Equations 11
2.1 Finite Iterative Algorithm and Convergence Analysis 12
2.2 Numerical Example . 24
2.3 Control Application 27
2.4 Conclusions 28
CHAPTER 3 Finite Iterative Algorithm to Coupled Operator Matrix Equations with Sub-Matrix Constrained 29
3.1 Iterative Method for Solving Problem 3.1 30
3.2 Iterative Method for Solving Problem 3.2 41
3.3 Numerical Example 42
3.4 Control Application 53
3.5 Conclusions 54
CHAPTER 4 MCGLS Iterative Algorithm to Linear Conjugate Matrix Equation 55
4.1 MCGLS Iterative Algorithm and Convergence Analysis 57
4.2 Numerical Example 66
4.3 Control Application 73
4.4 Conclusions 74
CHAPTER 5 MCGLS Iterative Algorithm to Linear Conjugate Transpose Matrix Equation 75
5.1 MCGLS Iterative Algorithm and Convergence Analysis 78
5.2 Numerical Example 90
5.3 Conclusions 95
CHAPTER 6 MCGLS Iterative Algorithm to Coupled Linear Operator Systems 97
6.1 Some Useful Lemmas 98
6.2 MCGLS Iterative Algorithm and Convergence Analysis 99
6.3 Numerical Examples 107
6.4 Conclusions 113
CHAPTER 7 Explicit Solutions to the Matrix Equation X ？ AXB = CY + R 115
7.1 Solutions to the Real Matrix Equation X ？ AXB = CY + R 115
7.2 Parametric Pole Assignment for Descriptor Linear Systems by P-D Feedback 124
7.3 Conclusions 128
CHAPTER 8 Explicit Solutions to the Nonhomogeneous Yakubovich-Transpose Matrix Equation 131
8.1 The First Approach 132
8.2 The Second Approach 140
8.3 Illustrative Example 142
8.4 Conclusions 143
CHAPTER 9 Explicit Solutions to the Matrix Equations XB 145
9.1 Real Matrix Equation XB ？ AX = CY 145
9.2 Quaternion-j-Conjugate Matrix Equation 148
9.2.1 Real Representation of a Quaternion Matrix 148
9.2.2 Solutions to the Quaternion j-Conjugate Matrix Equation 150
9.3 Conclusions 155
CHAPTER 10 Explicit Solutions to Linear Transpose Matrix Equation 157
10.1 Solutions to the Sylvester Transpose Matrix Equation 157
10.1.1 The First Case: A or B is Nonsingular 158
10.1.2 The Second Case: A and B are Nonsingular 162
10.2 Solutions to the Generalized Sylvester Transpose Matrix Equation 165
10.3 Algorithms for Solving Two Transpose Equations and Numerical Example 168
10.4 Application in Control Theory 174
10.5 Conclusions 175
References 177
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