Spectral analysis of block preconditioners for double saddle-point linear systems with application to PDE-constrained optimization
<|reference_start|>Spectral analysis of block preconditioners for double saddle-point linear systems with application to PDE-constrained optimization: In this paper, we describe and analyze the spectral properties of a symmetric positive definite inexact block preconditioner for a class of symmetric, double saddle-point linear systems.   We develop a spectral analysis of the preconditioned matrix, showing that its eigenvalues can be described in terms of the roots of a cubic polynomial with real coefficients.   We illustrate the efficiency of the proposed preconditioners, and verify the theoretical bounds, in solving large-scale PDE-constrained optimization problems.<|reference_end|>
@article{bergamaschi2024spectral,
    title={Spectral analysis of block preconditioners for double saddle-point
  linear systems with application to PDE-constrained optimization},
    author={Luca Bergamaschi and Angeles Martinez and John Pearson and Andreas
  Potschka},
    journal={arXiv preprint arXiv:2405.14605},
    year={2024},
    archivePrefix={arXiv},
    eprint={2405.14605},
    primaryClass={math.NA cs.NA}
}