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MATRIX REPRESENTATIONS OF INNER AND OUTER INVERSES (Operator monotone functions and related topics)

MATRIX REPRESENTATIONS OF INNER AND OUTER INVERSES (Operator monotone functions and related topics)
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J-inner matrix functions, interpolation and inverse problems for canonical systems, I: Foundations

Integral Equations and Operator Theory, 1997
Inverse problems for canonical systems of differential equations of the form \[ {dy \over dx} (x,\lambda) =i\lambda y(x,\lambda) H(x)J \] were studied; \(y(x,\lambda)\) is a \(k \times m\) matrix valued function, \(H(x)\) the Hermitian of the system, \(J\) is a constant \(m \times m\) signature matrix. The study was concentrated on the classes of \(J\)-
Damir Z Arov, Harry Dym, Arov Damir Z
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A family of iterative methods for computing the approximate inverse of a square matrix and inner inverse of a non-square matrix

Applied Mathematics and Computation, 2010
If \(V_0\) is an approximate inverse of a nonsingular square matrix \(A\) such that \(\|I-AV_0\|
Weiguo Li
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On the Block Independence in G–Inverse and Reflexive Inner Inverse of A Partitioned Matrix

Acta Mathematica Sinica, English Series, 2006
Suppose that \(A \in {\mathbb C}^{m\times n}, B \in {\mathbb C}^{m\times p}, C \in {\mathbb C}^{q\times n}\) and \(D \in {\mathbb C}^{q\times p}\), and the matrix \(M\) has the form \(M=\left ( \begin{matrix} A&B \\ C&D\end{matrix} \right )\). \textit{Y. Wang} [SIAM J. Matrix Anal. Appl. 19, No.
Liu, Yong Hui, Wei, Mu Sheng
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On the Block Independence in Reflexive Inner Inverse and M--P Inverse of Block Matrix

SIAM Journal on Matrix Analysis and Applications, 1998
Block independence of two, three, and four \(m\times n\) matrices in a generalized inverse satisfying some of the four Moore-Penrose (M-P) equations, is introduced. The independence of two and three matrices is characterized in the reflexive inner inverse and in the Moore-Penrose inverse. A conjecture is stated for four ordered matrices.
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Strongly Regular J-inner Matrix-valued Functions and Inverse Problems for Canonical Systems

2005
This paper provides an introduction to the role of strongly regular J-inner matrix-valued functions in the analysis of inverse problems for canonical integral and differential systems. A number of the main results that were developed in a series of papers by the authors are surveyed and examples and applications are presented, including an application ...
Damir Z Arov, Harry Dym, Arov Damir Z
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Weighted inner inverse for rectangular matrices

Quaestiones Mathematicae, 2022
To extend the notation of inner inverses, we dene weighted inner in-verses of a rectangular matrix. In particular, we introduce aW-weighted (B;C)-inner inverse of A, for given matrices A;W;B;C, and present some characterizations andconditions for its ...
Ratikanta Behera, Dijana Mosić, Jajati Keshari Sahoo   +2 more
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J-Inner matrix functions, interpolation and inverse problems for canonical systems, II: The inverse monodromy problem

Integral Equations and Operator Theory, 2000
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Arov, Damir Z., Dym, Harry
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J-inner matrix functions, interpolation and inverse problems for canonical systems, III: More on the inverse monodromy problem

Integral Equations and Operator Theory, 2000
The paper is a continuation of the study by \textit{D. Z. Arov} and \textit{H. Dym} [Integral Equations Oper. theory 29, No. 4, 373-454 (1997; Zbl 0902.30026)] (Part I), Part II ibid. 36, No. 1, 11-70 (2000; Zbl 0951.30029)]. The part I, Foundations, established a parametrization of the set of all solutions to the inverse monodromy for canonical ...
Arov, Damir Z., Dym, Harry
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