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Mathematics > Numerical Analysis

arXiv:2404.17168 (math)
[Submitted on 26 Apr 2024 (v1), last revised 3 Jul 2024 (this version, v2)]

Title:On the invertibility of matrices with a double saddle-point structure

Authors:Fatemeh P. A. Beik, Chen Greif, Manfred Trummer
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Abstract:We establish necessary and sufficient conditions for invertibility of symmetric three-by-three block matrices having a double saddle-point structure \fb{that guarantee the unique solvability of double saddle-point systems}. We consider various scenarios, including the case where all diagonal blocks are allowed to be rank deficient. Under certain conditions related to the nullity of the blocks and intersections of their kernels, an explicit formula for the inverse is derived.
Subjects: Numerical Analysis (math.NA)
MSC classes: 15A09, 15A03, 15A06
Cite as: arXiv:2404.17168 [math.NA]
  (or arXiv:2404.17168v2 [math.NA] for this version)
  https://doi.org/10.48550/arXiv.2404.17168

Submission history

From: Fatemeh Panjeh Ali Beik [view email]
[v1] Fri, 26 Apr 2024 05:46:54 UTC (18 KB)
[v2] Wed, 3 Jul 2024 03:45:59 UTC (18 KB)
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