Lars Grasedyck: rank-adaptive arithmetics for hierarchical matrices
We give a short introduction to the hierarchical
matrix structure and corresponding (formatted)
arithmetic. The focus is on the factorisation
of a large and sparse matrix that stems from an
elliptic partial differential equation.
We will observe that the hierarchical matrix
structure is well suited to store, e.g., the
Cholesky factor, but the blockwise rank is quite
heterogeneous. The rank-adaptive arithmetic that
we present chooses the rank for each block
adaptively. Numerical results for the 2d and 3d
Laplacian close the talk.