Open AccessOn the preconditioning of three-by-three block saddle point problems
Author(s) -
Hamed Aslani,
Davod Khojasteh Salkuyeh,
Fatemeh Panjeh Ali Beik
Publication year - 2021
Publication title -
filomat
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.449
H-Index - 34
eISSN - 2406-0933
pISSN - 0354-5180
DOI - 10.2298/fil2115181a
Subject(s) - preconditioner , generalized minimal residual method , mathematics , saddle point , coefficient matrix , eigenvalues and eigenvectors , block (permutation group theory) , iterative method , convergence (economics) , saddle , residual , matrix (chemical analysis) , mathematical optimization , mathematical analysis , algorithm , combinatorics , geometry , physics , materials science , quantum mechanics , economics , composite material , economic growth
We establish a new iterative method for solving a class of large and sparse linear systems of equations with three-by-three block coefficient matrices having saddle point structure. Convergence properties of the proposed method are studied in details and its induced preconditioner is examined for accelerating the convergence speed of generalized minimal residual (GMRES) method. More precisely, we analyze the eigenvalue distribution of the preconditioned matrix. Numerical experiments are reported to demonstrate the effectiveness of the proposed preconditioner.