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In this paper, we aim at giving efficient iterative methods for solving large sparse weakly nonlinear systems with complex symmetric coefficient matrices. Based on the separable property of the linear and nonlinear terms, and by combining with the double-parameter preconditioned MHSS (DPMHSS) method for linear systems, we propose the Picard-DPMHSS and nonlinear DPMHSS-like methods. Under suitable conditions, we establish convergence theorems for the Picard-DPMHSS and nonlinear DPMHSS-like methods. Numerical implementations show that both Picard-DPMHSS and nonlinear DPMHSS-like iteration methods are effective solvers for large sparse weakly nonlinear systems. |
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