This talk is devoted to the topic of subdivision schemes, a special class of iterative methods for
generating continuous curves and surfaces via the recursive application of suitable local refinement
rules to a coarse initial set of prescribed control points.
Due to their efficiency and simplicity of implementation, subdivision schemes are ones of the most
used representation models in computer graphics and animation. Recently, they have shown their
usefulness also in different areas of application like biomedical imaging and isogeometric analysis.
Important tools for both the construction of linear subdivision schemes and the analysis of their
properties are provided by classical numerical linear algebra techniques or adequate modifications
of them. In particular, the construction of interpolatory subdivision schemes capable of generating
curves and surfaces that pass through the initial set of prescribed control points, relies on algebraic
strategies that differ according to the symmetry properties of the underlying refinement rules. The
goal of this talk is to show some of the constructive strategies proposed in the literature for the
subclass of stationary, odd- and even-symmetric, interpolatory subdivision schemes of arbitrary