scholarly journals Convergence analysis for the equilibrium problems with numerical results

2014 ◽  
Vol 2014 (1) ◽  
Author(s):  
Sarawut Suwannaut ◽  
Atid Kangtunyakarn
Keyword(s):  
Convergence Analysis ◽  
Equilibrium Problems ◽  
Numerical Results

An Adaptive Combined Preconditioner with Applications in Radiation Diffusion Equations

2015 ◽  
Vol 18 (5) ◽  
pp. 1313-1335 ◽  
Author(s):  
Xiaoqiang Yue ◽  
Shi Shu ◽  
Xiao wen Xu ◽  
Zhiyang Zhou
Keyword(s):  
Convergence Analysis ◽  
Estimation Theory ◽  
Numerical Results ◽  
Diffusion Equations ◽  
Condition Numbers ◽  
Radiation Diffusion ◽  
Discrete Problems ◽  
Preconditioned Gmres

AbstractThe paper aims to develop an effective preconditioner and conduct the convergence analysis of the corresponding preconditioned GMRES for the solution of discrete problems originating from multi-group radiation diffusion equations. We firstly investigate the performances of the most widely used preconditioners (ILU(k) and AMG) and their combinations (Bco and Bco), and provide drawbacks on their feasibilities. Secondly, we reveal the underlying complementarity of ILU(k) and AMG by analyzing the features suitable for AMG using more detailed measurements on multiscale nature of matrices and the effect of ILU(k) on multiscale nature. Moreover, we present an adaptive combined preconditioner Bcoα involving an improved ILU(0) along with its convergence constraints. Numerical results demonstrate that Bcoα-GMRES holds the best robustness and efficiency. At last, we analyze the convergence of GMRES with combined preconditioning which not only provides a persuasive support for our proposed algorithms, but also updates the existing estimation theory on condition numbers of combined preconditioned systems.

scholarly journals A Predictor-Corrector Method for Solving Equilibrium Problems

2014 ◽  
Vol 2014 ◽  
pp. 1-11
Author(s):  
Zong-Ke Bao ◽  
Ming Huang ◽  
Xi-Qiang Xia
Keyword(s):  
Variational Inequalities ◽  
Convergence Analysis ◽  
Equilibrium Problems ◽  
Auxiliary Problem ◽  
The Other ◽  
Stationary Points ◽  
Stopping Criterion ◽  
Auxiliary Problem Principle ◽  
One Step ◽  
Predictor Corrector

We suggest and analyze a predictor-corrector method for solving nonsmooth convex equilibrium problems based on the auxiliary problem principle. In the main algorithm each stage of computation requires two proximal steps. One step serves to predict the next point; the other helps to correct the new prediction. At the same time, we present convergence analysis under perfect foresight and imperfect one. In particular, we introduce a stopping criterion which gives rise toΔ-stationary points. Moreover, we apply this algorithm for solving the particular case: variational inequalities.

scholarly journals Convergence analysis for combination of equilibrium problems and k-nonspreading multi-valued mappings

2021 ◽  
Author(s):  
Suhel Ahmad Khan ◽  
Kaleem Raza Kazmi ◽  
Watcharaporn Cholamjiak ◽  
Hemen Dutta
Keyword(s):  
Strong Convergence ◽  
Fixed Points ◽  
Convergence Analysis ◽  
Hybrid Method ◽  
Convergence Theorem ◽  
Equilibrium Problems ◽  
Solution Set ◽  
Strong Convergence Theorem ◽  
Numerical Example ◽  
Common Solution

We prove a strong convergence theorem for finding a common solution of a combination of equilibrium problems and the set of fixed points of a k-nonspreading multi-valued mapping by using shrinking projection hybrid method. Further, we give a numerical example to justify our main result and compare the shrinking areas of solution set after randomization.

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