scholarly journals Modified BAS iteration method for absolute value equation

2021 ◽  
Vol 7 (1) ◽  
pp. 606-616
Author(s):  
Cui-Xia Li ◽  
◽  
Long-Quan Yong ◽  
Keyword(s):  
Theoretical Analysis ◽  
Numerical Solution ◽  
Iteration Method ◽  
Numerical Experiments ◽  
Convergence Speed ◽  
Absolute Value Equation ◽  
Absolute Value ◽  
The Absolute ◽  
Block Diagonal

<abstract><p>In this paper, to improve the convergence speed of the block-diagonal and anti-block-diagonal splitting (BAS) iteration method, we design a modified BAS (MBAS) method to obtain the numerical solution of the absolute value equation. Theoretical analysis shows that under certain conditions the MBAS method is convergent. Numerical experiments show that the MBAS method is feasible.</p></abstract>

scholarly journals The Picard-HSS-SOR iteration method for absolute value equations

2020 ◽  
Vol 2020 (1) ◽  
Author(s):  
Lin Zheng
Keyword(s):  
Iteration Method ◽  
Numerical Experiments ◽  
Absolute Value Equation ◽  
Absolute Value Equations ◽  
Absolute Value ◽  
Convergence Results ◽  
Hss Iteration ◽  
The Absolute ◽  
Hss Iteration Method

AbstractIn this paper, we present the Picard-HSS-SOR iteration method for finding the solution of the absolute value equation (AVE), which is more efficient than the Picard-HSS iteration method for AVE. The convergence results of the Picard-HSS-SOR iteration method are proved under certain assumptions imposed on the involved parameter. Numerical experiments demonstrate that the Picard-HSS-SOR iteration method for solving absolute value equations is feasible and effective.

scholarly journals On Picard-SHSS iteration method for absolute value equation

2021 ◽  
Vol 6 (2) ◽  
pp. 1743-1753
Author(s):  
Shu-Xin Miao ◽  
◽  
Xiang-Tuan Xiong ◽  
Jin Wen
Keyword(s):  
Iteration Method ◽  
Absolute Value Equation ◽  
Absolute Value

scholarly journals Two-step modulus-based matrix splitting iteration method for horizontal linear complementarity problems

Filomat ◽  
2020 ◽  
Vol 34 (7) ◽  
pp. 2171-2184
Author(s):  
Lu Jia ◽  
Xiang Wang ◽  
Xuan-Sheng Wang
Keyword(s):  
Theoretical Analysis ◽  
Linear Complementarity Problem ◽  
Iteration Method ◽  
Complementarity Problem ◽  
Numerical Experiments ◽  
Complementarity Problems ◽  
Linear Complementarity Problems ◽  
Linear Complementarity ◽  
Matrix Splitting ◽  
Splitting Iteration Method

The modulus-based matrix splitting iteration has received substantial attention as a momentous tool for complementarity problems. For the purpose of solving the horizontal linear complementarity problem, we introduce the two-step modulus-based matrix splitting iteration method. We also show the theoretical analysis of the convergence. Numerical experiments illustrate the effectiveness of the proposed approach.

scholarly journals Absolute stability properties of the explicit linear 3-step formulae

1980 ◽  
Vol 9 (124) ◽  
Author(s):  
Zahari Zlatev ◽  
Ole Østerby
Keyword(s):  
Numerical Solution ◽  
Absolute Stability ◽  
Numerical Experiments ◽  
Parameter Family ◽  
Stability Properties ◽  
The Family ◽  
The Absolute

A three-parameter family of explicit linear 3-step formulae is derived. The conditions which ensure zero-stability of the formulae in the family are formulated. The absolute stability properties of the zero-stable formulae in the family are investigated both for p = 3 and p = 2 where p is the order of the formulae under consideration. Some numerical experiments are carried out in order to illustrate that formulae with good absolute stability properties can efficiently be used in the numerical solution of problems in which the absolute stability properties are dominant.

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