Abstract We present the successive linear Newton interpolation method for solving the large-scale nonlinear eigenvalue problems, establish locally linear convergence, and give the corresponding convergence factor of the method in terms of the left and right eigenvectors in this paper. To speed up the convergence rate, we develop the modified successive linear Newton interpolation method which updates the pole simultaneously. In addition, we propose the inexact versions of the (modified) successive linear Newton interpolation method to reduce the computational cost and analyze the convergence properties. Numerical results demonstrate the effectiveness of our proposed methods.

中文翻译：

---

求解大规模非线性特征值问题的逐次线性牛顿插值方法

摘要 提出求解大规模非线性特征值问题的逐次线性牛顿插值方法，建立局部线性收敛，并给出了该方法在左右特征向量方面对应的收敛因子。为了加快收敛速度​​，我们开发了改进的逐次线性牛顿插值方法，它同时更新极点。此外，我们提出了（修改的）连续线性牛顿插值方法的不精确版本，以降低计算成本并分析收敛特性。数值结果证明了我们提出的方法的有效性。