A quadratically convergent descent method for the absolute value equation Ax+B|x|=b

Abstract We propose a descent method for solving the absolute value equation A x + B | x | = b when the interval matrix [ A − | B | , A + | B | ] is regular. Without any additional assumption, we prove that (i) our method generates a bounded iteration sequence; (ii) any accumulation point of the iteration sequence is a solution of the absolute value equation; (iii) the whole iteration sequence converges to the solution of the absolute value equation quadratically. Some numerical results are reported.