廣義逆:理論與計(jì)算(英文版)

內(nèi)容概要

Generalized inverses arise in various applications in statistics,science and engineering,shch 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 writter for researchers in matrix theory,numerial linear algebra,parallel computatons and,particularly,the generalized inverses with application.And it can also be used as a text or reference for a graduate course.As prerequisties,we assume that reader is with basic linear algebra,matrix theory and functional analysis.

書籍目錄

PrefaceList of NotationsChapter 1 Equation Solving Generalized Inverses  1.1 The Moore-Pentose 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 Chapter1Chpater 2 Drazin Inverse  2.1 Drazin inverse  2.2 Group inverse  2.3 W-weighted Drazin inverse  Remarks on Chapter 2Chapter 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 3Chapter 4 The Reverse Order Law and Forward Order Law for the Generalized Inverses A(2)T,S  4.1 Inrroduction  4.2 Reverse order law  4.3 Forward order law  Remarks on Chapter 4Chpater 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  ……Chapter 6 The Parallel Algorithms for Computing the Generalized InversesChapter 7 Perturbation Analysis of the Moore-Penrose INverse and the Weighted Moore-InverseChapter 8 Perturbation Analysis of the Drazin Inverse and the Group InverseChapter 9 The Moore-Penrose Inverse of Linear OperatorsChapter 10 Drazin INverse of OperatorsChapter 11 W-weighted Drazin Inverse of OperatorsReferencesIndex

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