Integrating data and knowledge from multiple heterogeneous sources -- like databases, knowledge bases or specific software packages -- is often required for answering certain queries. Recently, a powerful framework for defining mediated views spanning multiple knowledge bases by a set of constrained rules was proposed [24, 4, 16]. We investigate the materialization of these views by unfolding the view definition and the efficient maintenance of the resulting materialized mediated view in case of updates. Thereby, we consider two kinds of updates: updates to the view and updates to the underlying sources. For each of these two cases several efficient algorithms maintaining materialized mediated views are given. We improve on previous algorithms like the DRed algorithm  and introduce a new fixpoint operator <i>W<inf>P</inf></i> which -- opposed to the standard fixpoint operator <i>T<inf>P</inf></i>  -- allows us to correctly capture the update's semantics without any recomputation of the materialized view.
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