The absolute value equation (AVE) is an important class of nonlinear and non-differentiable problems arising in scientific computing and applied engineering. Since the AVE can be equivalently transformed into a linear complementarity problem, developing efficient numerical methods for solving AVEs has attracted continuous research interest. This paper aims to construct efficient fixed point iterative methods for the AVE based on matrix splitting techniques.
A class of improved matrix-splitting fixed point iterative methods is proposed for solving the AVE. The proposed method adopts a two-step iterative framework and incorporates different matrix splitting strategies to improve convergence performance. Two sufficient conditions are established to guarantee the convergence of the proposed algorithms.
Numerical experiments are conducted to evaluate the effectiveness of the proposed methods. Three matrix splitting strategies are tested, and the results show that one of the proposed splitting schemes achieves better performance in terms of both iteration numbers (IT) and running time (CPU). These results demonstrate the feasibility and efficiency of the proposed two-step matrix-splitting fixed point iterative algorithms.
This paper develops an improved two-step fixed point iterative framework for solving absolute value equations by combining matrix splitting techniques with fixed point iteration. The proposed convergence conditions provide theoretical support for the algorithms, while the numerical results confirm their computational advantages over conventional approaches.
