SIAM Journal on Matrix Analysis and Applications, Volume 44, Issue 4, Page 1589-1618, December 2023.
Abstract. Generalized eigenvalue problems involving a singular pencil may be very challenging to solve, both with respect to accuracy and efficiency. While Part I presented a rank-completing addition to a singular pencil, we now develop two alternative methods. The first technique is based on a projection onto subspaces with dimension equal to the normal rank of the pencil while the second approach exploits an augmented matrix pencil. The projection approach seems to be the most attractive version for generic singular pencils because of its efficiency, while the augmented pencil approach may be suitable for applications where a linear system with the augmented pencil can be solved efficiently.

中文翻译：

---

解决奇异广义特征值问题。第二部分：投影和增强

《SIAM 矩阵分析与应用杂志》，第 44 卷，第 4 期，第 1589-1618 页，2023 年 12 月。
摘要。涉及单支铅笔的广义特征值问题解决起来可能非常具有挑战性，无论是在准确性还是效率方面。虽然第一部分提出了对单一铅笔的排名完成补充，但我们现在开发了两种替代方法。第一种技术基于维度等于铅笔正常等级的子空间的投影，而第二种方法则利用增强矩阵铅笔。由于其效率，投影方法似乎是通用奇异铅笔最有吸引力的版本，而增强铅笔方法可能适合可以有效求解具有增强铅笔的线性系统的应用。