Classification of Double Saddle-Point Systems
This work offers a systematic classification and theoretical foundation for double saddle-point systems, which is useful for researchers working on numerical methods for such systems.
The paper classifies symmetric double saddle-point systems into block-arrow and block-tridiagonal forms, providing invertibility conditions, spectral properties, and block preconditioners within a general framework.
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.