Researchers Develop Biparametric Preconditioner for Large Double Saddle Point Problems

Researchers have developed a biparametric preconditioning technique designed for large, sparse, non-symmetric, and non-singular double saddle point problems. The open-access research article was authored by Hamed Aslani, Mehdi Najafi Kalyani, and Davod Khojasteh Salkuyeh, and was published on 14 November 2026.

The proposed preconditioner is induced through a stationary iteration method and is based on a two-parameterized block LU factorization of the system’s coefficient matrix.

To substantiate the theoretical foundation of the approach, the authors derived several convergence results for the stationary iteration method.

In addition to deriving convergence guarantees, the research team analyzed the spectral features exhibited by the preconditioned matrix.

Finally, the authors conjuncted the presented biparametric preconditioner with the Generalized Minimal Residual method, known as GMRES. Numerical experiments reported in the paper demonstrated the satisfactory performance of the preconditioner when applied to these linear systems. The citable, peer-reviewed, and accepted research was shared early with a permanent DOI, and this version remains subject to further edits before being replaced automatically by the final Version of Record.

Subject of Research: Numerical linear algebra and preconditioning for double saddle point problems

Article Title: A parameterized block LU preconditioning for double saddle point problems

Article References: Aslani, H., Kalyani, M. N., & Salkuyeh, D. K. (2026). A parameterized block LU preconditioning for double saddle point problems. Scientific Reports. https://doi.org/10.1038/s41598-026-72620-w

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DOI: 10.1038/s41598-026-72620-w

Keywords: double saddle point problems, biparametric preconditioning, block LU factorization, stationary iteration method, GMRES method, sparse matrices, non-symmetric systems, non-singular matrices, spectral features, preconditioned matrix, convergence analysis, numerical linear algebra, coefficient matrix, iterative solvers, Scientific Reports, computational mathematics