scholarly journals Convergence analysis of a gradient iterative algorithm with optimal convergence factor for a generalized Sylvester-transpose matrix equation

2021 ◽  
Vol 6 (8) ◽  
pp. 8477-8496
Author(s):  
Nunthakarn Boonruangkan ◽  
◽  
Pattrawut Chansangiam
Keyword(s):  
Convergence Analysis ◽  
Iterative Algorithm ◽  
Matrix Equation ◽  
Convergence Factor ◽  
Optimal Convergence

scholarly journals The convergence of a numerical method for total variation flow

2021 ◽  
Vol 15 ◽  
pp. 174830262110113
Author(s):  
Qianying Hong ◽  
Ming-jun Lai ◽  
Jingyue Wang
Keyword(s):  
Finite Difference ◽  
Difference Scheme ◽  
Numerical Method ◽  
Convergence Analysis ◽  
Total Variation ◽  
Iterative Algorithm ◽  
Finite Difference Scheme ◽  
Gradient Flow ◽  
Time Dependent ◽  
Total Variation Flow

We present a convergence analysis for a finite difference scheme for the time dependent partial different equation called gradient flow associated with the Rudin-Osher-Fetami model. We devise an iterative algorithm to compute the solution of the finite difference scheme and prove the convergence of the iterative algorithm. Finally computational experiments are shown to demonstrate the convergence of the finite difference scheme.

scholarly journals Convergence analysis of gradient-based iterative algorithms for a class of rectangular Sylvester matrix equations based on Banach contraction principle

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Adisorn Kittisopaporn ◽  
Pattrawut Chansangiam ◽  
Wicharn Lewkeeratiyutkul
Keyword(s):  
Spectral Radius ◽  
Matrix Equation ◽  
Iterative Algorithms ◽  
Banach Contraction Principle ◽  
Contraction Principle ◽  
Convergence Factor ◽  
Sylvester Matrix ◽  
Iteration Matrix ◽  
Banach Contraction ◽  
The Matrix

AbstractWe derive an iterative procedure for solving a generalized Sylvester matrix equation $AXB+CXD = E$ A X B + C X D = E , where $A,B,C,D,E$ A , B , C , D , E are conforming rectangular matrices. Our algorithm is based on gradients and hierarchical identification principle. We convert the matrix iteration process to a first-order linear difference vector equation with matrix coefficient. The Banach contraction principle reveals that the sequence of approximated solutions converges to the exact solution for any initial matrix if and only if the convergence factor belongs to an open interval. The contraction principle also gives the convergence rate and the error analysis, governed by the spectral radius of the associated iteration matrix. We obtain the fastest convergence factor so that the spectral radius of the iteration matrix is minimized. In particular, we obtain iterative algorithms for the matrix equation $AXB=C$ A X B = C , the Sylvester equation, and the Kalman–Yakubovich equation. We give numerical experiments of the proposed algorithm to illustrate its applicability, effectiveness, and efficiency.

Convergence analysis of an iterative algorithm to solve system of nonlinear stochastic Itô‐Volterra integral equations

2020 ◽  
Vol 43 (8) ◽  
pp. 5212-5233 ◽  
Author(s):  
Masoud Saffarzadeh ◽  
Mohammad Heydari ◽  
Ghasem Barid Loghmani
Keyword(s):  
Convergence Analysis ◽  
Integral Equations ◽  
Iterative Algorithm ◽  
Volterra Integral Equations

scholarly journals The optimal convergence factor of the gradient based iterative algorithm for linear matrix equations

Filomat ◽  
2012 ◽  
Vol 26 (3) ◽  
pp. 607-613 ◽  
Author(s):  
Xiang Wang ◽  
Dan Liao
Keyword(s):  
Iterative Algorithm ◽  
Numerical Experiments ◽  
Linear Matrix ◽  
Matrix Equations ◽  
Convergence Factor ◽  
Gradient Based ◽  
Gradient Type ◽  
And Mathematics ◽  
Computers And Mathematics ◽  
Linear Matrix Equations

A hierarchical gradient based iterative algorithm of [L. Xie et al., Computers and Mathematics with Applications 58 (2009) 1441-1448] has been presented for finding the numerical solution for general linear matrix equations, and the convergent factor has been discussed by numerical experiments. However, they pointed out that how to choose a best convergence factor is still a project to be studied. In this paper, we discussed the optimal convergent factor for the gradient based iterative algorithm and obtained the optimal convergent factor. Moreover, the theoretical results of this paper can be extended to other methods of gradient-type based. Results of numerical experiments are consistent with the theoretical findings.

Convergence analysis of a general iterative algorithm for finding a common solution of split variational inclusion and optimization problems

2018 ◽  
Vol 79 (3) ◽  
pp. 801-824 ◽  
Author(s):  
Kanokwan Sitthithakerngkiet ◽  
Jitsupa Deepho ◽  
Juan Martínez-Moreno ◽  
Poom Kumam
Keyword(s):  
Convergence Analysis ◽  
Iterative Algorithm ◽  
Optimization Problems ◽  
Variational Inclusion ◽  
Common Solution

scholarly journals Iterative algorithm for the reflexive solutions of the generalized Sylvester matrix equation

2019 ◽  
Vol 27 (1) ◽  
Author(s):  
Mohamed A. Ramadan ◽  
Naglaa M. El–shazly ◽  
Basem I. Selim
Keyword(s):  
Iterative Algorithm ◽  
Matrix Equation ◽  
Sylvester Matrix Equation ◽  
Sylvester Matrix ◽  
Generalized Sylvester Matrix Equation
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