Geometric convergence of iterative methods for a problem with \(M\)-matrices and diagonal multivalued operators. (English) Zbl 0998.65064
A finite-dimensional problem with several \(M\)-matrices and diagonal maximal monotone operators is studied. The problem includes variational inequalities with \(M\)-matrices. Existence of a unique solution is studied as well as the convergence and geometric rate of convergence for a class of iterative methods. For instance the Schwarz alternating type methods are considered.
Then the author applies the general results to a mesh scheme for a dam problem. Parallel iterative methods are proposed based on domain decomposition. The geometric convergence is proved. All results of this paper are theoretical.
Then the author applies the general results to a mesh scheme for a dam problem. Parallel iterative methods are proposed based on domain decomposition. The geometric convergence is proved. All results of this paper are theoretical.
Reviewer: Yves Cherruault (Paris)
MSC:
65K10 | Numerical optimization and variational techniques |
65N06 | Finite difference methods for boundary value problems involving PDEs |
65F10 | Iterative numerical methods for linear systems |
65N12 | Stability and convergence of numerical methods for boundary value problems involving PDEs |
65N55 | Multigrid methods; domain decomposition for boundary value problems involving PDEs |
49J40 | Variational inequalities |