Absolute value equations : theoretical and Numerical study

Abstract

In this thesis, we highlight, on one hand the unique solvability of the absolute value equations where some sufficient weaker conditions are given. These results are also generalized to the unique solvability of horizontal and standard linear complementarity problems. On the other hand, for its numerical solution, Picard’s iterative and preconditioned conjugate gradient methods are proposed. Finally, some numerical results are given to confirm the efficiency of our proposed approaches for solving the AVEs.