On the uniform boundedness and convergence of generalized, Moore-Penrose and group inverses

Filomat ◽  
2017 ◽  
Vol 31 (19) ◽  
pp. 5993-6003 ◽  
Author(s):  
Lanping Zhu ◽  
Changpeng Zhu ◽  
Qianglian Huang
Keyword(s):  
Operator Theory ◽  
Generalized Inverse ◽  
Matrix Theory ◽  
Uniform Boundedness ◽  
Generalized Inverses ◽  
Convergence Theorems ◽  
Linear Subspaces ◽  
Group Inverses ◽  
Stable Perturbation ◽  
The Relationship

This paper concerns the relationship between uniform boundedness and convergence of various generalized inverses. Using the stable perturbation for generalized inverse and the gap between closed linear subspaces, we prove the equivalence of the uniform boundedness and convergence for generalized inverses. Based on this, we consider the cases for the Moore-Penrose inverses and group inverses. Some new and concise expressions and convergence theorems are provided. The obtained results extend and improve known ones in operator theory and matrix theory.

EP Operators and Generalized Inverses

1975 ◽  
Vol 18 (3) ◽  
pp. 327-333 ◽  
Author(s):  
Stephen L. Campbell ◽  
Carl D. Meyer
Keyword(s):  
Hilbert Space ◽  
Canonical Form ◽  
Generalized Inverse ◽  
Generalized Inverses ◽  
Space Setting ◽  
The Relationship

AbstractThe relationship between properties of the generalized inverse of A, A†, and of the adjoint of A, A*, are studied. The property that A†A and AA† commute, called (E4), is investigated. (E4) generalizes the property of A being EPr. A canonical form and a formula for A† are given if a matrix A is (E4). Results are in a Hilbert space setting whenever possible. Examples are given.

Inverse complements and strongly unit regular elements

2021 ◽  
pp. 2250190
Author(s):  
Umashankara Kelathaya ◽  
Savitha Varkady ◽  
Manjunatha Prasad Karantha
Keyword(s):  
Partial Order ◽  
Regular Element ◽  
Generalized Inverse ◽  
Generalized Inverses ◽  
Order Unit ◽  
Regular Elements ◽  
Strongly Regular ◽  
Minus Partial Order

In this paper, the notion of “strongly unit regular element”, for which every reflexive generalized inverse is associated with an inverse complement, is introduced. Noting that every strongly unit regular element is unit regular, some characterizations of unit regular elements are obtained in terms of inverse complements and with the help of minus partial order. Unit generalized inverses of given unit regular element are characterized as sum of reflexive generalized inverses and the generators of its annihilators. Surprisingly, it has been observed that the class of strongly regular elements and unit regular elements are the same. Also, several classes of generalized inverses are characterized in terms of inverse complements.

scholarly journals Generalized inverses over integral domains. II. group inverses and Drazin inverses

1991 ◽  
Vol 146 ◽  
pp. 31-47 ◽  
Author(s):  
K. Manjunatha Prasad ◽  
K.P.S. Bhaskara Rao ◽  
R.B. Bapat
Keyword(s):  
Generalized Inverses ◽  
Integral Domains ◽  
Group Inverses

ROLLER-COASTER FAILURE RATES AND MEAN RESIDUAL LIFE FUNCTIONS WITH APPLICATION TO THE EXTENDED GENERALIZED INVERSE GAUSSIAN MODEL

2010 ◽  
Vol 25 (1) ◽  
pp. 103-118 ◽  
Author(s):  
Ramesh C. Gupta ◽  
Weston Viles
Keyword(s):  
Failure Rate ◽  
Generalized Inverse ◽  
Residual Life ◽  
Gaussian Model ◽  
Change Points ◽  
Mean Residual Life ◽  
Additional Parameter ◽  
Inverse Gaussian ◽  
Generalized Inverse Gaussian ◽  
The Relationship

The investigation in this article was motivated by an extended generalized inverse Gaussian (EGIG) distribution, which has more than one turning point of the failure rate for certain values of the parameters. In order to study the turning points of a failure rate, we appeal to Glaser's eta function, which is much simpler to handle. We present some general results for studying the reationship among the change points of Glaser's eta function, the failure rate, and the mean residual life function (MRLF). Additionally we establish an ordering among the number of change points of Glaser's eta function, the failure rate, and the MRLF. These results are used to investigate, in detail, the monotonicity of the three functions in the case of the EGIG. The EGIG model has one additional parameter, δ, than the generalized inverse Gaussian (GIG) model's three parameters; see Jorgensen [7]. It has been observed that the EGIG model fits certain datasets better than the GIG of Jorgensen [7]. Thus, the purpose of this article is to present some general results dealing with the relationship among the change points of the three functions described earlier. The EGIG model is used as an illustration.

The Application Research of the Matrix in Multi-Parameter Measurement FBGs

2012 ◽  
Vol 461 ◽  
pp. 702-706
Author(s):  
Xiao Xia Wang ◽  
Chun Ying Wu ◽  
Win Lin Wang
Keyword(s):  
Condition Number ◽  
Matrix Theory ◽  
Parameter Measurement ◽  
Application Research ◽  
Fbg Sensor ◽  
The Matrix ◽  
The Relationship ◽  
Different Thickness

The sensitivity of the FBG sensor based on multi-parameter measurement was established and determined by the matrix theory. The condition number of matrix was proposed to deduced the relationship among the measurement multi-parameters of the coated FBGs. The ill-conditioned matrix parameters can be removed, and the relationship between the FBGs sensitivities and many attribute parameters of the coated-FBG was found. As indicated by the experiment, when measure the temperature and the pressure at the same time, the sensitivities of FBG is higher by coated with different thickness of copper,and the second radius is less than 0.4mm,and the FBGs sensitivities can be improved to 5~10 times.

scholarly journals Stable perturbation in Banach algebras

2007 ◽  
Vol 83 (2) ◽  
pp. 271-284 ◽  
Author(s):  
Yifeng Xue
Keyword(s):  
Banach Algebra ◽  
Error Estimates ◽  
Generalized Inverse ◽  
Invertible Element ◽  
Banach Algebras ◽  
Gap Function ◽  
Drazin Inverse ◽  
C Algebras ◽  
Stable Perturbation ◽  
Unital Banach Algebra

AbstractLet be a unital Banach algebra. Assume that a has a generalized inverse a+. Then is said to be a stable perturbation of a if . In this paper we give various conditions for stable perturbation of a generalized invertible element and show that the equation is closely related to the gap function . These results will be applied to error estimates for perturbations of the Moore-Penrose inverse in C*–algebras and the Drazin inverse in Banach algebras.

The Information Optimal Algorithm Based on Poly-Scaled Wavelet Wraps and Wavelet Frames with Finite Support

2011 ◽  
Vol 204-210 ◽  
pp. 1759-1762
Author(s):  
Tong Qi Zhang
Keyword(s):  
Multiresolution Analysis ◽  
Operator Theory ◽  
Matrix Theory ◽  
Integral Transform ◽  
Optimal Algorithm ◽  
Higher Dimensions ◽  
Wavelet Frames ◽  
Finite Support ◽  
Multi Scale ◽  
Vector Valued

In this paper, we propose the notion of vector-valued multiresolution analysis and the vector-valued mutivariate wavelet wraps with multi-scale factor of spaceL2(Rn, Cv), which are ge- neralizations of multivariate wavelet wraps. An approach for designing a sort of biorthogonal vec- tor-valued wavelet wraps in higher dimensions is presented and their biorthogonality trait is charac- -terized by virtue of integral transform, matrix theory, and operator theory. Two biorthogonality formulas regarding these wavelet wraps are established.

scholarly journals Relevance of Matrices and Image Processing

2020 ◽  
Vol 2 (2) ◽  
pp. 126-130
Author(s):  
Vishali . ◽  
Harpal Singh ◽  
Priyanka Kaushal
Keyword(s):  
Image Processing ◽  
Matrix Theory ◽  
Specific Information ◽  
Higher Dimension ◽  
Digital Form ◽  
Good Insight ◽  
Relationship Of ◽  
The Relationship

An image is formed by the small bit of information namely pixel which is stored in the form of an array or a matrix. An image is converted into a digital form and some operations are carried out on this so that an improved image can be obtained and some specific information regarding the same can be recovered too; this procedure is known as image processing. Different processes in image processing involve different methods and operations applied. Matrix Theory has great importance in the operations applied in image processing. This manuscript is focused on the relationship of matrix theory and image processing in various applications of image processing. In order to understand the higher dimension matrices in image processing, some applications are considered to give a good insight.

Obstacle Avoidance Algorithm for Redundant Manipulators Based on Weighted Generalized Inverse

2017 ◽  
Vol 872 ◽  
pp. 303-309
Author(s):  
Hai Rui Cao ◽  
Xiao Qin Gu ◽  
Chu Hong Yu
Keyword(s):  
Obstacle Avoidance ◽  
Generalized Inverse ◽  
Redundant Manipulators ◽  
Continuous Transition ◽  
Secondary Tasks ◽  
Field Measuring ◽  
Joint Limits ◽  
The Relationship ◽  
Dangerous Level ◽  
Weighted Generalized Inverse

In this paper, a gradient projection method for redundant robot manipulators based on weighted generalized inverse was presented. By weighting the Jacobian matrix and gradient, not only the obstacles, but also the joint limits could be avoided. In the process of obstacle avoidance, the evaluation function called danger field measuring the dangerous level between the manipulator and obstacles was used and improved. According to the relationship between the value of danger field and the preset threshold, a smooth and continuous transition between the primary and secondary tasks is allowed. This method was proved to be effective by numerical simulations in Matlab.

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