A robust parameterized enhanced shift-splitting preconditioner for three-by-three block saddle point problems

This paper proposes a new parameterized enhanced shift-splitting (PESS) preconditioner to solve the three-by-three block saddle point problem (SPP). Additionally, we introduce a local PESS (LPESS) preconditioner by relaxing the PESS preconditioner. Necessary and sufficient criteria are established f...

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Bibliographic Details
Published in:Journal of computational and applied mathematics 2025-05, Vol.459, p.116358, Article 116358
Main Authors: Ahmad, Sk. Safique, Khatun, Pinki
Format: Article
Language:English
Subjects:
GMRES
Krylov subspace iterative process
Preconditioner
Robust
Saddle point problem
Shift-splitting
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Summary:This paper proposes a new parameterized enhanced shift-splitting (PESS) preconditioner to solve the three-by-three block saddle point problem (SPP). Additionally, we introduce a local PESS (LPESS) preconditioner by relaxing the PESS preconditioner. Necessary and sufficient criteria are established for the convergence of the proposed PESS iterative process for any initial guess. Furthermore, we meticulously investigate the spectral bounds of the PESS and LPESS preconditioned matrices. Moreover, empirical investigations have been performed for the sensitivity analysis of the proposed PESS preconditioner, which unveils its robustness. Numerical experiments are carried out to demonstrate the enhanced efficiency and robustness of the proposed PESS and LPESS preconditioners compared to the existing state-of-the-art preconditioners.
ISSN:0377-0427
DOI:10.1016/j.cam.2024.116358