On GSOR-based iteration methods for solving weakly nonlinear systems with complex symmetric coefficient matrices

In this paper, two methods based on generalized successive overrelaxation (GSOR) for solving weakly nonlinear systems with complex coefficient matrices are proposed: Picard-accelerated GSOR (P-AGSOR) and Picard-preconditioned GSOR (P-PGSOR) methods. Theoretical analysis demonstrates the local convergence properties of the two methods under appropriate assumptions. Numerical examples confirm the effectiveness and superiority of the two methods.