Iterative methods for computing generalized inverses and splittings of operators

2009 ◽  
Vol 208 (1) ◽  
pp. 186-188 ◽  
Author(s):  
Biljana Načevska
Keyword(s):  
Iterative Methods ◽  
Generalized Inverses

scholarly journals Generalized Inverses Estimations by Means of Iterative Methods with Memory

Mathematics ◽  
2019 ◽  
Vol 8 (1) ◽  
pp. 2
Author(s):  
Santiago Artidiello ◽  
Alicia Cordero ◽  
Juan R. Torregrosa ◽  
María P. Vassileva
Keyword(s):  
Iterative Methods ◽  
Generalized Inverses ◽  
Drazin Inverse ◽  
Nonsingular Matrix ◽  
Type Method ◽  
The Matrix ◽  
Nonlinear Matrix ◽  
First Time ◽  
With Memory ◽  
Theoretical Results

A secant-type method is designed for approximating the inverse and some generalized inverses of a complex matrix A. For a nonsingular matrix, the proposed method gives us an approximation of the inverse and, when the matrix is singular, an approximation of the Moore–Penrose inverse and Drazin inverse are obtained. The convergence and the order of convergence is presented in each case. Some numerical tests allowed us to confirm the theoretical results and to compare the performance of our method with other known ones. With these results, the iterative methods with memory appear for the first time for estimating the solution of a nonlinear matrix equations.

scholarly journals ZNN models for computing matrix inverse based on hyperpower iterative methods

Filomat ◽  
2017 ◽  
Vol 31 (10) ◽  
pp. 2999-3014 ◽  
Author(s):  
Igor Stojanovic ◽  
Predrag Stanimirovic ◽  
Ivan Zivkovic ◽  
Dimitrios Gerontitis ◽  
Xue-Zhong Wang
Keyword(s):  
Neural Network ◽  
Iterative Methods ◽  
Generalized Inverses ◽  
Convergence Properties ◽  
Matrix Inverse ◽  
The Family ◽  
The Matrix ◽  
Zhang Neural Network ◽  
Implementation In Matlab

Our goal is to investigate and exploit an analogy between the scaled hyperpower family (SHPI family) of iterative methods for computing the matrix inverse and the discretization of Zhang Neural Network (ZNN) models. A class of ZNN models corresponding to the family of hyperpower iterative methods for computing generalized inverses is defined on the basis of the discovered analogy. The Simulink implementation in Matlab of the introduced ZNN models is described in the case of scaled hyperpower methods of the order 2 and 3. Convergence properties of the proposed ZNN models are investigated as well as their numerical behavior.

scholarly journals Iterative methods for computing generalized inverses related with optimization methods

2005 ◽  
Vol 78 (2) ◽  
pp. 257-272 ◽  
Author(s):  
Dragan S. Djordjević ◽  
Predrag S. Stanimirović
Keyword(s):  
Iterative Methods ◽  
Unconstrained Minimization ◽  
Optimization Methods ◽  
Second Order ◽  
Steepest Descent ◽  
Generalized Inverses ◽  
Minimization Methods ◽  
Second Order Methods

AbstractWe develop several iterative methods for computing generalized inverses using both first and second order optimization methods in C*-algebras. Known steepest descent iterative methods are generalized in C*-algebras. We introduce second order methods based on the minimization of the norms ‖Ax − b‖2 and ‖x‖2 by means of the known second order unconstrained minimization methods. We give several examples which illustrate our theory.

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