Materialized views can bring important performance benefits when querying XML documents. In the presence of XML document changes, materialized views need to be updated to faithfully reflect the changed document. In this work, we present an algebraic approach for propagating source updates to XML materialized views expressed in a powerful XML tree pattern formalism. Our approach differs from the state of the art in the area in two important ways. First, it relies on set-oriented, algebraic operations, to be contrasted with node-based previous approaches. Second, it exploits state-of-the-art features of XML stores and XML query evaluation engines, notably XML structural identifiers and associated structural join algorithms. We present algorithms for determining how updates should be propagated to views, and highlight the benefits of our approach over existing algorithms through a series of experiments.