On unique solvability and Picard’s iterative method for absolute value equations

In this paper, we deal with unique solvability and numerical solution ofabsolute value equations (AVE),Ax−B|x|=b, (A,B∈Rn×n,b∈Rn).Under some weaker conditions, a simple proof is given for unique solvabilityof AVE. Furthermore, we demonstrate with an example that these results arereliable to detect unique solvability of AVE. These results are also extendedto unique solvability of standard and horizontal linear complementarity prob-lems. Finally, we suggest a Picard iterative method to compute an approx-imated solution of some uniquely solvable AVE problems where its globallylinear convergence is guaranteed via one of our weaker sufficient condition.