A class of iteration methods based on the HSS for Toeplitz systems of weakly nonlinear equations

作者：Zhu, Mu-Zheng; Zhang, Guo-Feng^*

来源：Journal of Computational and Applied Mathematics, 2015, 290: 433-444.

DOI：10.1016/j.cam.2015.05.027

• Toeplitz
• Weakly nonlinear systems
• HSS iteration method
• Inner/outer iteration
• Centrosymmetric and skew-centrosymmetric
• Local convergence

For Toeplitz systems of weakly nonlinear equations, combining the separability and strong dominance between the linear and the nonlinear terms with the Hermitian and skew-Hermitian splitting (HSS) iteration technique, we establish two nonlinear composite iteration schemes, called Picard-cSSS and nonlinear cSSS-like iteration methods, which are based on a special case of the HSS, where the symmetric partH = 1/2 (A + A(T)) is a centrosymmetric matrix and the skew-symmetric part H = 1/2 (A - A(T)) is a skew-centrosymmetric matrix, The advantages of these methods are that they can transfer the linear sub-systems involved in inner iteration to two linear systems of half an order, besides, fast methods are available for computing the two half-steps involved in the inner iteration. Numerical results are provided, to further show that both Picard-cSSS and nonlinear cSSS-like iteration methods are feasible and effective.

• 出版日期2015-12-15
• 单位河西学院; 兰州大学