Book ChapterDOI
A Unified Operator Theory of Generalized Inverses
M. Zuhair Nashed,G.F. Votruba +1 more
- pp 1-109
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TLDR
In this article, a unified approach to generalized inverses of linear operators is presented, with particular emphasis on algebraic, topological, extremal, and proximinal properties.Abstract:
The main purpose of this paper is to develop a unified approach to generalized inverses of linear operators, with particular emphasis on algebraic, topological, extremal, and proximinal properties.read more
Citations
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Journal ArticleDOI
Hyers—Ulam stability of functional equations in several variables
TL;DR: In this paper, a survey about Hyers-Ulam stability of functional equations and systems in several variables is presented, with a focus on the stability of the Ulam model.
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Operator-theoretic and computational approaches to Ill-posed problems with applications to antenna theory
TL;DR: A general framework for regularization and approximation methods for ill-posed problems is developed in this paper, where three levels in the resolution processes are distinguished and emphasized: philosophy of resolution, regularization-approximation schema, and regularization algorithms.
Journal ArticleDOI
Inner, outer, and generalized inverses in banach and hilbert spaces
TL;DR: In this paper, a unified theory of generalized inverse operators on Banach spaces is developed, with bounded inner and bounded outer inverses, new extremal and proximinal properties and a few related observations and properties.
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Frame expansions in separable banach spaces
TL;DR: In this paper, the authors characterize Banach frames and X d -frames in separable Banach spaces, and relate them to series expansions in Banach space, and show that they do not share all the nice properties of frames in Hilbert spaces.
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Solving and factoring boundary problems for linear ordinary differential equations in differential algebras
TL;DR: An algebra of linear integro-differential operators is constructed that is expressive enough for specifying regular boundary problems with arbitrary Stieltjes boundary conditions as well as their solution operators.
References
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Journal ArticleDOI
A Generalized inverse for matrices
TL;DR: A generalization of the inverse of a non-singular matrix is described in this paper as the unique solution of a certain set of equations, which is used here for solving linear matrix equations, and for finding an expression for the principal idempotent elements of a matrix.
Journal ArticleDOI
On best approximate solutions of linear matrix equations
TL;DR: In this paper, it was shown how to define a generalized inverse of a non-singular matrix, which has relevance to the statistical problem of finding the best approximate solution of inconsistent systems of equations by the method of least squares.
Journal ArticleDOI
Pseudo-Inverses in Associative Rings and Semigroups
TL;DR: In this paper, Pseudo-inverses in Associative Rings and Semigroups are discussed in the context of semigroups, and pseudo-Inverses are shown to be pseudo-dual in a semigroup.
Journal ArticleDOI
Orthogonality and linear functionals in normed linear spaces
TL;DR: The notion of orthogonality was introduced in this paper, which is a generalization of the notion of homogeneous homogeneous elements to normed linear spaces, and has been studied extensively in the literature.