Minimum Residual BAS Iteration Method for Solving the System of Absolute Value Equations

In this work, by applying the minimum residual technique to the block-diagonal and anti-block-diagonal splitting (BAS) iteration scheme, an iteration method named minimum residual BAS (MRBAS) is proposed to solve a two-by-two block system of nonlinear equations arising from the reformulation of the system of absolute value equations (AVEs). The theoretical analysis shows that the MRBAS iteration method is convergent under suitable conditions. Numerical results demonstrate the feasibility and the effectiveness of the MRBAS iteration method.