Generalized Inverses : Theory and Computations

Author: Wang Guorong
Language: English
ISBN/ISSN: 7030124375
Published on: 2004-01
Hardcover

List of Notations
Chapter 1 Equation Solving Generalized Inverses
1.1 The Moore-Penrose inverse
1.2 {i,j,k}inverses
1.3 The generalized inverses with prescribed range and null space
1.4 Weighted Moore-Penrose inverses
1.5 Bott-Duffin inverses and generalized Bott-Duffin inverses
Remarks on Chapter 1
Chapter 2 Drazin Inverse
2.1 Drazin Inverse
2.2 Group inverses
2.3 W-weighted Drazin Inverse
Remarks on Chapter 2
Chapter 3 The Generalization of Cramer Rule and the Minors of the 3.1 Generalized Inverses
3.2 The nonsingularity of bordered matrices
3.3 Cramer rule for the solution of a linear equation
3.4 Cramer rule for the solution of a matrix equation
3.5 The determinantal expressions of the minors of the generalized inverses
Remarks on Chapter 3
Chapter 4 The Reverse Order Law and Forward Order Law for the Generalized Inverses A(2)T,S
4.1 Introduction
4.2 Reverse order law
4.3 Forward order law
Remarks on Chapter 4
Chapter 5 Computational Aspects of the Generalized Inverses
5.1 Methods based on full rank factorizations
5.2 Singular value decompositions and(M,N)singular value decompositions
5.3 Generalized inverses of sums and partitioned matrices
5.4 Imbedding methods
5.5 Finite algorithms
Remarks on Chapter 5
Chapter 6 The parallel Algorithms for Computing the Generalized Inverses
6.1 The model of parallel processors
6.2 Measures of the performance of parallel algorithms
6.3 Parallel algorithms
6.4 Equivalence theorem
Remarks on Chapter 6
Chapter 7 Perturbation Analysis of the Moore-Penrose Inverse and the Weighted Moore-Penrose Inverse
7.1 Perturbation bound
7.2 Continuity
7.3 Rand-preserving modification
7.4 Condition number
7.5 Expression for the perturbation of the weighted Moore-Penrose inverses
Remarks on Chapter 7
Chapter 8 Perturbation Analysis of the Drazin Inverse and the Group Inverse
8.1 Perturbation bound for the Drazin inverse
8.2 Continuity of the Drazin inverse
8.3 Core-rank preserving modification of the Drazin inverse
8.4 Condition number of the Drazin inverse
8.5 Perturbatio bound for the group inverse
Remarks on Chapter 8
Chapter 9 The Moore-Penrose Inverse of Linear Operators
9.1 Definition and basic properties
9.2 Representation theorem
9.3 Computational methods
Remarks on Chapter 9
Chapter 10 Drazin Inverse of Operators
10.1 Definition and basic properties
10.2 Representation theorem
10.3 Computational procedures
10.4 Perturbation bound
Remarks on Chapter 10
Chapter 11 W-weighted Drazin Inverse of Operators
11.1 Definition and basic properties
11.2 Representation theorem
11.3 Computational procedures
11.4 Perturbation bound
Remarks on Chapter 11
References
Index