We derive bounds on the eigenvalues of a generic form of double saddle-point matrices. The bounds are expressed in terms of extremal eigenvalues and singular values of the associated block matrices. Inertia and algebraic multiplicity of eigenvalues are considered as well. The analysis includes bounds for preconditioned matrices based on block diagonal preconditioners using Schur complements, and it is shown that in this case the eigenvalues are clustered within a few intervals bounded away from zero. Analysis for approximations of Schur complements is included. Some numerical experiments validate our analytical findings.

翻译：我们从一种通用形式的双马鞍基质的外观值中得出外观值的界限,其表达方式是极端的外观值和相关区块基质的单值,也考虑了异性值和异性代数值的异性值。分析包括基于使用Schur补充材料的区块二马座基质的前提条件基质的界限,并表明在此情况下,双马座基质值在远离零的几段间隔内被分组。包括了对Schur补充材料近似值的分析。一些数字实验证实了我们的分析结论。