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Geometric convergence of iterative methods for variational inequalities with $$M$$-matrices and diagonal monotone operators. (English) Zbl 1041.65055
Lapin, A. (ed.) et al., Numerical methods for continuous casting and related problems. Proceedings of the Russian-Finnish workshop held in Kazan, Russia, April 14–18, 2001. Kazan: DAS Publisher (ISBN 5-8185-0023-3/pbk). Tr. Mat. Tsentra im. N. I. Lobachevskogo 9, 63-72 (2001).
Summary: The iterative solution of the problem $Au+B\gamma+ \delta=f, \quad\gamma\in Cu,\quad\delta\in Du,$ with $$M$$-matrices $$A,B$$ and diagonal maximal monotone (multivalued) operators is $$C,D$$ is studied. Geometric (or, linear) rate of convergence is proved for several classes of iterative algorithms under some additional assumptions imposed to input data. Applications of general results to mesh schemes for free boundary problems are considered.
For the entire collection see [Zbl 1011.00041].

MSC:
 65K10 Numerical optimization and variational techniques 49J40 Variational inequalities 49M25 Discrete approximations in optimal control 35R35 Free boundary problems for PDEs 65N06 Finite difference methods for boundary value problems involving PDEs 65F10 Iterative numerical methods for linear systems
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