Limited memory preconditioners for nonsymmetric systems

Sylvain Mercier (1) , Serge Gratton (2, 3) , Nicolas Tardieu (1) , Xavier Vasseur (4)

1 IMSIA - UMR 9219 - Institut des Sciences de la mécanique et Applications industrielles
2 Toulouse INP - Institut National Polytechnique (Toulouse)
3 ENSEEIHT - Ecole Nationale Supérieure d'Electrotechnique, d'Electronique, d'Informatique, d'Hydraulique et de Télécommunications
4 ISAE-SUPAERO - Institut Supérieur de l'Aéronautique et de l'Espace

This paper presents a class of limited memory preconditioners (LMPs) for solving linear systems of equations with multiple nonsymmetric matrices and multiple right-hand sides. These preconditioners based on limited memory quasi-Newton formulas require a small number k of linearly independent vectors. They may be used to improve an existing first-level preconditioner and are especially worth considering when the solution of a sequence of linear systems with slowly varying left-hand sides is addressed.

Keywords: preconditioning; Krylov methods

Keywords: méthode de Krylov; solveur non-linéaire; préconditionnement

Domains: Engineering Sciences [physics]; Mechanics [physics.med-ph]; Structural mechanics [physics.class-ph]

Sylvain Mercier, Serge Gratton, Nicolas Tardieu, Xavier Vasseur. Limited memory preconditioners for nonsymmetric systems. 13e colloque national en calcul des structures, Université Paris-Saclay, May 2017, Giens, Var, France. ⟨hal-01923673⟩