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arXiv · 2405.14605

Spectral analysis of block preconditioners for double saddle-point linear systems with application to PDE-constrained optimization

Luca Bergamaschi·Angeles Martinez·John Pearson·Andreas Potschka
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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.

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Luca Bergamaschi, Angeles Martinez, John Pearson, Andreas Potschka. 2024-05-23. Spectral analysis of block preconditioners for double saddle-point linear systems with application to PDE-constrained optimization. https://arxiv.org/abs/2405.14605

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