Generalized Inverses and Applications
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Generalized Inverses and Applications

Proceedings of an Advanced Seminar Sponsored by the Mathematics Research Center, the University of Wisconsin—Madison, October 8 - 10, 1973

  1. 1,068 pages
  2. English
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  4. Only available on web
eBook - PDF

Generalized Inverses and Applications

Proceedings of an Advanced Seminar Sponsored by the Mathematics Research Center, the University of Wisconsin—Madison, October 8 - 10, 1973

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About This Book

Generalized Inverses and Applications, contains the proceedings of an Advanced Seminar on Generalized Inverses and Applications held at the University of Wisconsin-Madison on October 8-10, 1973 under the auspices of the university's Mathematics Research Center. The seminar provided a forum for discussing the basic theory of generalized inverses and their applications to analysis and operator equations. Numerical analysis and approximation methods are considered, along with applications to statistics and econometrics, optimization, system theory, and operations research. Comprised of 14 chapters, this book begins by describing a unified approach to generalized inverses of linear operators, with particular reference to algebraic, topological, extremal, and proximinal properties. The reader is then introduced to the algebraic aspects of the generalized inverse of a rectangular matrix; the Fredholm pseudoinverse; and perturbations and approximations for generalized inverses and linear operator equations. Subsequent chapters deal with various applications of generalized inverses, including programming, games, and networks, as well as estimation and aggregation in econometrics. This monograph will be of interest to mathematicians and students of mathematics.

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Information

Publisher
Academic Press
Year
2014
ISBN
9781483270296
Topic
Mathematics
Subtopic
Pre-Calculus
Index
Mathematics

Table of contents

  1. Front Cover
  2. Generalized Inverses and Applications
  3. Copyright Page
  4. Table of Contents
  5. Foreword
  6. Preface
  7. Chapter 1. A Unified Operator Theory of Generalized Inverses
  8. Chapter 2. Algebraic Aspects of the Generalized Inverse of a Rectangular Matrix
  9. Chapter 3. Some Topics in Generalized Inverses of Matrices
  10. Chapter 4. The Fredholm Pseudoinverse— An Analytic Episode in the History of Generalized Inverses
  11. Chapter 5. A Role of the Pseudoinverse in Analysis
  12. Chapter 6. Aspects of Generalized Inverses in Analysis and Regularization
  13. Chapter 7. Methods for Computing the Moorse-Penrose Generalized Inverse, and Related Matters
  14. Chapter 8. Differentiation of Pseudoinverses, Separable Nonlinear Least Square Problems and Other Tales
  15. Chapter 9. Perturbations and Approximations for Generalized Inverses and Linear Operator Equations
  16. Chapter 10. The Operator Pseudoinverse in Control and Systems Identification
  17. Chapter 11. Applications of Generalized Inverses to Programming,Games and Networks
  18. Chapter 12. Statistical Applications of the Pseudo Inverse
  19. Chapter 13. Estimation and Aggregation in Econometrics: An Application of the Theory of Generalized Inverses
  20. Chapter 14. Annotated Bibliography on Generalized Inverses and Applications
  21. Index