Generalized Inverses and Applications - 1st Edition - ISBN: 9780125142502, 9781483270296

Generalized Inverses and Applications

1st Edition

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

Editors: M. Zuhair Nashed
eBook ISBN: 9781483270296
Imprint: Academic Press
Published Date: 28th January 1976
Page Count: 1068
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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.

Table of Contents



I. Theory of Generalized Inverses

A Unified Operator Theory of Generalized Inverses

Algebraic Aspects of the Generalized Inverse of a Rectangular Matrix

Some Topics in Generalized Inverses of Matrices

II. Generalized Inverses in Analysis

The Fredholm Pseudoinverse — An Analytic Episode in the

History of Generalized Inverses

A Role of the Pseudo-Inverse in Analysis

Aspects of Generalized Inverses in Analysis and Regularization

III. Computational Methods and Approximation Theory

Methods for Computing the Moore-Penrose Generalized Inverse, and Related Matters

Differentiation of Pseudoinverses, Separable Nonlinear Least Squares Problems and Other Tales

Perturbations and Approximations for Generalized Inverses and Linear Operator Equations

IV. Applications

The Operator Pseudoinverse in Control and Systems Identification

Applications of Generalized Inverses to Programming, Games and Networks

Statistical Applications of the Pseudo Inverse

Estimation and Aggregation in Econometrics: An Application of the Theory of Generalized Inverses

Annotated Bibliography on Generalized Inverses and Applications



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© Academic Press 1976
Academic Press
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About the Editor

M. Zuhair Nashed

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