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Error bounds for linear complementarity problems of weakly chained diagonally dominant B-matrices
1College of Science, Guizhou Minzu University, Guiyang, Guizhou 550025 P.R. China.
Journal of Inequalities and Applications
|February 21, 2017
Summary
New error bounds for the linear complementarity problem (LCP) were developed for weakly chained diagonally dominant B-matrices. These bounds improve upon existing results, offering enhanced accuracy for LCP solutions.
Area of Science:
- Numerical Analysis
- Optimization Theory
- Matrix Theory
Background:
- The linear complementarity problem (LCP) is a fundamental problem in mathematical programming and game theory.
- Existing error bounds for LCPs involving specific matrix classes may lack sufficient tightness.
Purpose of the Study:
- To derive novel and improved error bounds for the linear complementarity problem.
- To focus on the specific class of weakly chained diagonally dominant B-matrices.
Main Methods:
- Theoretical analysis to establish new error bounds.
- Utilizing properties of weakly chained diagonally dominant B-matrices.
Main Results:
- New error bounds for the linear complementarity problem were successfully obtained.
- The proposed error bounds demonstrate superiority over previously established results.
Conclusions:
- The derived error bounds offer a more accurate estimation for LCP solutions with the specified matrix properties.
- Numerical examples confirm the advantages and improved performance of the new bounds.
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