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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.
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
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
- No. of pages:
- © Academic Press 1976
- 28th January 1976
- Academic Press
- eBook ISBN: