On eigenvalue distribution of constraint-preconditioned symmetric saddle point matrices. (English) Zbl 1274.65084
Numer. Linear Algebra Appl. 19, No. 4, 754-772 (2012); corrigendum ibid. 21, No. 1, 171-174 (2014).
Bounds on the eigenvalues of preconditioned symmetric saddle point matrices are presented. The derived bounds slightly improve results known so far. Two classes of inexact saddle point preconditioners are considered: full and triangular inexact constrant preconditioner, which both rely on approximating the inverse of the \((1,1)\) block and of its Schur complement in the saddle point matrix. Numerical experiments illustrate the result on problems arising in discretisations of a coupled consolidation problem in porous media.
Reviewer: Pavel Jiránek (Toulous)
MSC:
| 65F08 | Preconditioners for iterative methods |
| 65F10 | Iterative numerical methods for linear systems |
| 15A42 | Inequalities involving eigenvalues and eigenvectors |
| 76S05 | Flows in porous media; filtration; seepage |
Keywords:
saddle point problem; iterative method; inexact constraint preconditioners; eigenvalue bounds; Schur complement; numerical experiments; consolidation problem in porous mediaSoftware:
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