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PreprintCC BY-SA 4.0arXiv

Block diagonal preconditioners for arrow-shaped multiple saddle-point linear systems

  • Luca Bergamaschi
  • Michele Bergamaschi
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Abstract

We consider multiple saddle-point linear systems with block-arrow structure. We analyze exact and inexact Schur complement based block diagonal preconditioner, by characterizing the eigenvalues of the preconditioned matrices in terms of the zeros of specific rational functions. Numerical results onto large tests coming from liquid crystal modeling and PDE-constrained optimization validate the obtained eigenvalue bounds

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Cite

BibTeXRIS
BibTeX
@misc{bergamaschi2026block,
  title = {{Block diagonal preconditioners for arrow-shaped multiple saddle-point linear systems}},
  author = {Luca Bergamaschi and Michele Bergamaschi},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.17940},
  eprint = {2610.17940},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.17940},
  note = {CC BY-SA 4.0},
}
RIS
TY  - UNPB
TI  - Block diagonal preconditioners for arrow-shaped multiple saddle-point linear systems
AU  - Luca Bergamaschi
AU  - Michele Bergamaschi
PY  - 2026
DA  - 2026/10/13
PB  - arXiv
DO  - 10.48550/arxiv.2610.17940
UR  - https://arxiv.org/abs/2610.17940
AB  - We consider multiple saddle-point linear systems with block-arrow structure. We analyze exact and inexact Schur complement based block diagonal preconditioner, by characterizing the eigenvalues of the preconditioned matrices in terms of the zeros of specific rational functions. Numerical results onto large tests coming from liquid crystal modeling and PDE-constrained optimization validate the obtained eigenvalue bounds
ER  -