In this work, we give an effective preconditioned numerical method to solve the discretized linear system, which is obtained from the space fractional complex Ginzburg–Landau equations. The coefficient matrix of the linear system is the sum of a symmetric tridiagonal matrix and a complex Toeplitz matrix. The preconditioned iteration method has computational superiority since we can use the fast Fourier transform and the circulant preconditioner to solve the discretized linear system. Numerical examples are tested to illustrate the advantage of the proposed preconditioned numerical method.

中文翻译：

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非线性复Ginzburg-Landau方程的预处理方法

在这项工作中，我们给出了一种有效的预处理数值方法来求解从空间分数复数 Ginzburg-Landau 方程获得的离散化线性系统。线性系统的系数矩阵是对称三对角矩阵和复托普利茨矩阵之和。预条件迭代法具有计算优势，因为我们可以使用快速傅立叶变换和循环预条件器来求解离散化线性系统。对数值例子进行了测试，以说明所提出的预处理数值方法的优点。