The numerical solution of singular generalized eigenvalue problems is still challenging. In Hochstenbach, Mehl, and Plestenjak, Solving Singular Generalized Eigenvalue Problems by a Rank-Completing Perturbation, SIMAX 2019, a rank-completing perturbation was proposed and a related bordering of the singular pencil. For large sparse pencils, we propose an LU factorization that determines a rank completing perturbation that regularizes the pencil and that is then used in the shift-and-invert Arnoldi method to obtain eigenvalues nearest a shift. Numerical examples illustrate the theory and the algorithms.

翻译：奇异广义特征值问题的数值求解仍然具有挑战性。在Hochstenbach、Mehl和Plestenjak于SIMAX 2019发表的《通过秩完备化摄动求解奇异广义特征值问题》一文中，提出了一种秩完备化摄动及其相关的奇异矩阵束边界方法。针对大规模稀疏矩阵束，我们提出了一种LU分解方法，该方法可确定一个使矩阵束正则化的秩完备化摄动，随后将其用于位移-逆Arnoldi方法中以获取最接近给定位移的特征值。数值算例验证了相关理论与算法的有效性。