Direct versus iterative methods for fixed-point implementation of matrix inversion

2004 ◽  
Author(s):  
M. Ylinen ◽  
A. Burian ◽  
J. Takala
Keyword(s):  
Fixed Point ◽  
Iterative Methods ◽  
Matrix Inversion

scholarly journals Approximation theorems of a solution of amperometric enzymatic reactions based on Green’s fixed point normal-S iteration

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Khanitin Muangchoo-in ◽  
Kanokwan Sitthithakerngkiet ◽  
Parinya Sa-Ngiamsunthorn ◽  
Poom Kumam
Keyword(s):  
Fixed Point ◽  
Boundary Value Problems ◽  
Iterative Methods ◽  
Dynamical Problem ◽  
Enzymatic Reactions ◽  
Nonlinear Dynamical ◽  
Numerical Examples ◽  
Approximation Theorems ◽  
Kinetics Of ◽  
Nonlinear Dynamical Problem

AbstractIn this paper, the authors present a strategy based on fixed point iterative methods to solve a nonlinear dynamical problem in a form of Green’s function with boundary value problems. First, the authors construct the sequence named Green’s normal-S iteration to show that the sequence converges strongly to a fixed point, this sequence was constructed based on the kinetics of the amperometric enzyme problem. Finally, the authors show numerical examples to analyze the solution of that problem.

Verification of Iterative Methods for the Linear Complementarity Problem

2016 ◽  
pp. 545-580 ◽  
Author(s):  
H. Saberi Najafi ◽  
S. A. Edalatpanah
Keyword(s):  
Fixed Point ◽  
Iterative Methods ◽  
Linear Complementarity Problem ◽  
Numerical Experiments ◽  
Linear Complementarity Problems ◽  
Linear Complementarity ◽  
Convergence Results ◽  
Fixed Point Principle ◽  
Preconditioned Iterative ◽  
Preconditioned Iterative Methods

In the present chapter, we give an overview of iterative methods for linear complementarity problems (abbreviated as LCPs). We also introduce these iterative methods for the problems based on fixed-point principle. Next, we present some new properties of preconditioned iterative methods for solving the LCPs. Convergence results of the sequence generated by these methods and also the comparison analysis between classic Gauss-Seidel method and preconditioned Gauss-Seidel (PGS) method for LCPs are established under certain conditions. Finally, the efficiency of these methods is demonstrated by numerical experiments. These results show that the mentioned models are effective in actual implementation and competitive with each other.

scholarly journals Performance of relaxed iterative methods for image deblurring problems

2019 ◽  
Vol 13 ◽  
pp. 174830261986173 ◽  
Author(s):  
Jae H Yun
Keyword(s):  
Fixed Point ◽  
Iterative Methods ◽  
Total Variation ◽  
Numerical Experiments ◽  
Krylov Subspace ◽  
Image Deblurring ◽  
Total Variation Regularization ◽  
L1 Norm ◽  
Split Bregman ◽  
Relaxation Parameters

In this paper, we consider performance of relaxation iterative methods for four types of image deblurring problems with different regularization terms. We first study how to apply relaxation iterative methods efficiently to the Tikhonov regularization problems, and then we propose how to find good preconditioners and near optimal relaxation parameters which are essential factors for fast convergence rate and computational efficiency of relaxation iterative methods. We next study efficient applications of relaxation iterative methods to Split Bregman method and the fixed point method for solving the L1-norm or total variation regularization problems. Lastly, we provide numerical experiments for four types of image deblurring problems to evaluate the efficiency of relaxation iterative methods by comparing their performances with those of Krylov subspace iterative methods. Numerical experiments show that the proposed techniques for finding preconditioners and near optimal relaxation parameters of relaxation iterative methods work well for image deblurring problems. For the L1-norm and total variation regularization problems, Split Bregman and fixed point methods using relaxation iterative methods perform quite well in terms of both peak signal to noise ratio values and execution time as compared with those using Krylov subspace methods.

scholarly journals On the Positive Definite Solutions of a Nonlinear Matrix Equation

2013 ◽  
Vol 380-384 ◽  
pp. 1434-1438
Author(s):  
Ming Hui Wang ◽  
Chun Yan Liang ◽  
Shan Rui Hu
Keyword(s):  
Fixed Point ◽  
Matrix Equation ◽  
Fixed Point Theory ◽  
Point Theory ◽  
Positive Definite ◽  
Matrix Inversion ◽  
Nonlinear Matrix Equation ◽  
Nonlinear Matrix

In this paper, the nonlinear matrix equation is investigated. Based on the fixed-point theory, the boundary and the existence of the solution with the case are discussed. An algorithm that avoids matrix inversion with the case is proposed.

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