论文标题
解决奇异的广义特征值问题。第二部分：投影和增强
Solving singular generalized eigenvalue problems. Part II: projection and augmentation
论文作者
论文摘要
在准确性和效率方面，涉及单数铅笔的广义特征值问题可能非常具有挑战性。虽然我对单数铅笔提出了排名的补充，但我们现在开发了两种替代方法。第一种技术是基于对尺寸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的基质铅笔。由于其效率，投影方法似乎是通用单数铅笔的最吸引人的版本，而增强铅笔方法可能适用于可以有效地解决带有增强铅笔的线性系统的应用。
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.
