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  广义逆:理论与计...
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Generalized inverses arise in various applications in statistics,science and engineering，such as least squares approximation，singular differential and difference equations,singular control，Markov chains and ill-posed problems.This book contains the latest developments in the theory and computations of generalized inverses.
This book was written for researchers in matrix theory,numerical linear algebra，parallel computations and，particularly,the generalized inverses with applications.And it can also be used as a text or reference for a graduate course.As prerequisites,we assume that reader iS with basic linear algebra.matrix theory and functional analysis.

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• Preface
  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 inverse
  1.5 Bott-Duffin inverse and generalized Bott-Duffin inverse
  Remarks on Chapter 1
  Chapter 2 Drazin Inverse
  2.1 Drazin inverse
  2.2 Group inverse
  2.3 W-weighted Drazin inverse
  Remarks on Chapter 2
  Chapter 3 The Generalization of Cramer Rule and the Minors of the Generalized Inverses
  3.1 The nonsingularity of bordered matrices
  3.2 Cramer rule for the solution of a linear equation
  3.3 Cramer rule for the solution of a matrix equation
  3.4 The determinantal expressions of the generalized inverses and projectors
  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 AT，S的(2)次方
  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 Mpore-Penrose Inverse and the Weighted Moore-Penrose Inverse
  7.1 Perturbation bound
  7.2 Continuity
  7.3 Rank-preserving modification
  7.4 Condition number
  7.5 Expression for the perturbation of the weighted Moore-Penrose inverse
  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 Perturbation 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