Reza Sharafdini

In this thesis, the numerical solution of generalized large and sparse absolute power equations is investigated. These equations are important in numerical analysis and scientific computations due to their relevance to linear complement problems, linear programming, and optimization models. The main focus of the thesis is on the study and implementation of the fixed-point iteration method based on the transfer-split method for solving generalized absolute power equations. In this method, the original equation is rewritten as a block nonlinear system and then solved using a parametric iterative process. The suffcient convergence conditions of the method under appropriate assumptions are reviewed and analyzed. In the numerical section, the effciency of the transfer-fission method is compared with the fixed-point iteration method and the pseudo-SOR method in terms of the number of iterations, execution time, and relative residual. The numerical results show that the pseudo-SOR method usually reaches the stopping criterion with a lower number of iterations and computational time in the studied examples.