标题： 预处理对称多重鞍点矩阵的特征值界 显示英文标题

标题： Eigenvalue bounds for preconditioned symmetric multiple saddle-point matrices

摘要： 我们研究了具有块对角预条件矩阵的对称块三对角多重鞍点线性系统的特征值界。我们将已知结果从$3 \times 3$块系统 [Bradley 和 Greif, IMA J. Numer. Anal. 43 (2023)] 和$4 \times 4$系统 [Pearson 和 Potschka, IMA J. Numer. Anal. 44 (2024)] 推广到任意数量的块。此外，我们的结果推广了 [Sogn 和 Zulehner, IMA J. Numer. Anal. 39 (2018)] 中针对零对角块的任意数量块所开发的界。还使用摄动论提供了当舒尔补近似时界值的扩展。对于双重鞍点线性系统也得到了实用的界值。数值实验验证了我们的发现。 显示英文摘要

摘要： We develop eigenvalue bounds for symmetric, block tridiagonal multiple saddle-point linear systems, preconditioned with block diagonal matrices. We extend known results for $3 \times 3$ block systems [Bradley and Greif, IMA J.\ Numer. Anal. 43 (2023)] and for $4 \times 4$ systems [Pearson and Potschka, IMA J. Numer. Anal. 44 (2024)] to an arbitrary number of blocks. Moreover, our results generalize the bounds in [Sogn and Zulehner, IMA J. Numer. Anal. 39 (2018)], developed for an arbitrary number of blocks with null diagonal blocks. Extension to the bounds when the Schur complements are approximated is also provided, using perturbation arguments. Practical bounds are also obtained for the double saddle-point linear system. Numerical experiments validate our findings.