<p>The operator splitting methods exhibit excellent ability in solving large-scale absolute value equations, especially the inexact versions. However, two important parameters that play a crucial role in numerical performance are not judiciously addressed. One is the parameter in the residual, which is fixed as a constant. The other one is the error tolerance parameter in the inaccuracy criterion, which is hard to determine since it involves the estimation of an error bound constant. In this paper, by using a different potential function in convergence analysis, we design two new error criteria whose parameters do not rely on any estimation of other parameters. The algorithms are flexible in the sense that the accuracy criterion is relative, and the parameter is arbitrary in an interval. Our methods avoid the task of presetting a sequence of parameters in the absolute error accuracy criterion and the estimation of an upper bound involving the input data in other relative accuracy criteria. We also present the linear rate of convergence of proposed algorithms under the error bound condition. We report some promising numerical results.</p>