1. Error bounds and a condition number for the absolute value equations
- Author
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Milan Hladík, Moslem Zamani, Research Group: Operations Research, and Econometrics and Operations Research
- Subjects
Absolute value equation ,convergence rate ,Optimization and Control (math.OC) ,General Mathematics ,FOS: Mathematics ,interval matrix ,error bounds ,linear complementarity problem ,Mathematics - Optimization and Control ,Software ,condition number - Abstract
Due to their relation to the linear complementarity problem, absolute value equations have been intensively studied recently. In this paper, we present error bound conditions for absolute value equations. Along with the error bounds, we introduce a condition number. We consider general scaled matrix p-norms, as well as particular p-norms. We discuss basic properties of the condition number, including its computational complexity. We present various bounds on the condition number, and we give exact formulae for special classes of matrices. Moreover, we consider matrices that appear based on the transformation from the linear complementarity problem. Finally, we apply the error bound to convergence analysis of two methods for solving absolute value equations.
- Published
- 2023