Abstract We derive a simple procedure for solving systems of linear equations arising from the linearization of the VTN-phase stability problem. Using the structure of the Hessian matrix, the solution is obtained by sequential usage of the Sherman-Morrison formula. The great advantage of the method is that the system of equation can be solved without even assembling the system. The performance and the speed-up of the computation is demonstrated on several examples of different complexity.

中文翻译：

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使用 Sherman-Morrison 迭代对 VTN 相位稳定性问题进行线性化时出现的线性系统的有效解

摘要 我们推导出一个简单的程序来求解由 VTN 相位稳定性问题的线性化产生的线性方程组。使用 Hessian 矩阵的结构，通过依次使用 Sherman-Morrison 公式获得解。该方法的一大优点是无需组装系统即可求解方程组。在几个不同复杂度的例子中展示了计算的性能和加速。