Geodesic
A new block triangular preconditioner for three-by-three block saddle-point problem
Applications of Mathematics, Tome 69 (2024) no. 1, pp. 67-91.

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In this paper, to solve the three-by-three block saddle-point problem, a new block triangular (NBT) preconditioner is established, which can effectively avoid the solving difficulty that the coefficient matrices of linear subsystems are Schur complement matrices when the block preconditioner is applied to the Krylov subspace method. Theoretical analysis shows that the iteration method produced by the NBT preconditioner is unconditionally convergent. Besides, some spectral properties are also discussed. Finally, numerical experiments are provided to show the effectiveness of the NBT preconditioner.
DOI : 10.21136/AM.2023.0289-22
Classification : 65F08, 65F10, 65F50
Keywords: three-by-three block saddle-point problems; matrix splitting; convergence; preconditioning, GMRES method 
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Li, Jun; Xiong, Xiangtuan. A new block triangular preconditioner for three-by-three block saddle-point problem. Applications of Mathematics, Tome 69 (2024) no. 1, pp. 67-91. doi : 10.21136/AM.2023.0289-22. http://geodesic.mathdoc.fr/articles/10.21136/AM.2023.0289-22/

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