I'm trying to implement a Conjugate Gradient solver using Hierarchical Basis Functions, following this paper.In section 3 the paper says that the hierarchical basis matrix $S$ can be decomposed into a series of very sparse matrices $S = S_1S_2...S_{L-1}$  but it doesn't tell the exact structure of these matrices $S_i$, nor in which way they are sparse.Therefore: What is the structure of $S_i$ (I assume they are all similar in a way)? Why is $S_i$ sparse? What is the interpretation of applying $S_i$ to a vector?
Conjugate Gradient with Hierarchical Basis Functions: How can the hierarchical base be decomposed?
linear algebra;pde;finite element;basis set;computer vision