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Many problems in operations research, management science, and engineering fields lead to the solution of absolute value equations. In this study, we propose two new iteration methods for solving absolute value equations $Ax-\left|x\right|=b$, where $A\in {ℝ}^{n\times n}$ is an $M$-matrix or strictly diagonally dominant matrix, $b\in {ℝ}^n$ and $x\in {ℝ}^n$ is an unknown solution vector. Furthermore, we discuss the convergence of the proposed two methods under suitable assumptions. Numerical experiments are given to verify the feasibility, robustness and effectiveness...