Spectral analysis of block preconditioners for double saddle-point linear systems with application to PDE-constrained optimization
Abstract
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.
- Publication:
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arXiv e-prints
- Pub Date:
- May 2024
- DOI:
- 10.48550/arXiv.2405.14605
- arXiv:
- arXiv:2405.14605
- Bibcode:
- 2024arXiv240514605B
- Keywords:
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- Mathematics - Numerical Analysis