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Efficient numerical solution of mixed finite element discretizations by adaptive multilevel methods

Ronald H.W. Hoppe, Barbara Wohlmuth (1995)

Applications of Mathematics

We consider mixed finite element discretizations of second order elliptic boundary value problems. Emphasis is on the efficient iterative solution by multilevel techniques with respect to an adaptively generated hierarchy of nonuniform triangulations. In particular, we present two multilevel solvers, the first one relying on ideas from domain decomposition and the second one resulting from mixed hybridization. Local refinement of the underlying triangulations is done by efficient and reliable a...

Ein effizienter Algorithmus zur iterativen Einschliessung der inversen Matrix

Jürgen Herzberger (1987)

Aplikace matematiky

Es wird ein kombinierter Algorithmus zur iterativen Einschlissung der Inversen einer Matrix beschrieben. Es handelt sich dabei um eine intervallmässige Version des Schulz'schen Verfahrens. Es wird bewiesen, dass der Algorithmus genauso effizient ist wie ein hisher bekannter aus [2], dass er aber in Bezug auf den akkumulierten Rundungsfehler dem bisherigen Vorgehen vorzuziehen ist. Ein numerisches Beispiel wird gegeben.

Enclosures for the solution set of parametric interval linear systems

Milan Hladík (2012)

International Journal of Applied Mathematics and Computer Science

We investigate parametric interval linear systems of equations. The main result is a generalization of the Bauer-Skeel and the Hansen-Bliek-Rohn bounds for this case, comparing and refinement of both. We show that the latter bounds are not provable better, and that they are also sometimes too pessimistic. The presented form of both methods is suitable for combining them into one to get a more efficient algorithm. Some numerical experiments are carried out to illustrate performances of the methods....

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