Classification of Double Saddle-Point Systems
Susanne Bradley, Chen Greif
TL;DR
This paper classifies symmetric double saddle-point systems by matrix structure, discussing applications, invertibility, spectral properties, and preconditioners within a general framework.
Contribution
It introduces a novel classification based on block-arrow and block-tridiagonal matrix forms for symmetric double saddle-point systems.
Findings
Classification into block-arrow and block-tridiagonal forms
Analysis of invertibility and spectral properties
Development of relevant block preconditioners
Abstract
We offer a classification of a broad and practically relevant class of symmetric double saddle-point system. At the core of the paper is the division of the associated matrices into ``block-arrow'' and ``block-tridiagonal'' forms. We describe relevant applications, invertibility conditions, spectral properties, and block preconditioners. Our discussion is kept within a general framework rather than tailored to specific applications.
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