DFPI presented at Third Joint SIAM/CAIMS Annual Meeting

July 25, 2025

Our PhD student Jérémy Kalfoun (EDMH, CentraleSupelec, Paris-Saclay University) will present his recent work at the Third Joint SIAM/CAIMS Annual Meeting, held next week in Montréal, Canada.

His talk presents our recent formalization of deflation techniques applied to fixed-point iterations, leading to the introduction of the Deflated Fixed-Point Iterations (DFPI) framework and the new PARMRES method. These approaches are designed for the efficient and robust solution of large linear systems arising in computational physics and optimization.

DFPI provide a flexible framework extending classical fixed-point iterations by incorporating deflation allowing:

• – A formal convergence analysis, independent of the projection space and operator.
• – A precise connection with Krylov subspace methods such as GMRES and CG and stabilization techniques such as RPM.
• – New strategies in terms of vector selection.

On the numerical side, the results are particularly promising:

• – DFPI achieves Krylov-like convergence rates with significantly reduced storage.
• – In several test cases, it matches or outperforms GMRES in terms of calculation time.
• – The proposed dynamic deflation strategies combine the efficiency of spectral deflation with the robustness of Krylov-based minimization.

These advances contribute to the design of more efficient and stable solvers for large-scale simulation, with promising perspectives for adaptive strategies and long-term integration into real-world applications.

Come meet Jérémy in Montréal, here is the abstract!