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In this paper we introduce an algorithm based on a sparse grid adaptiverefinement, for the approximation of the eigensolutions to parametric problemsarising from elliptic partial differential equations. In particular, we areinterested in detecting the crossing of the hypersurfaces describing theeigenvalues as a function of the parameters. The a priori matching is followedby an a posteriori verification, driven by a suitably defined error indicator.At a given refinement level, a sparse grid approach is adopted for theconstruction of the grid of the next level, by using the marking given by the aposteriori indicator. Various numerical tests confirm the good performance ofthe scheme.

A greedy MOR method for the tracking of eigensolutions to parametric elliptic PDEs