"The Technique of Hierarchical Matrices"
Prof. Dr. Dr. h.c. Wolfgang Hackbusch (Max-Planck-Institut für Mathematik, Leipzig)
Matrices of large size arise in particular from elliptic partial differential
equations and integral equations. In the former case one can make use of the
sparsity, in the latter case a standard treatment of the matrices already
leads to storage problems. The technique of hierarchical matrices allows
to organise the storage as well as all matrix operations (including inversion)
with almost linear complexity. The hierarchical matrix operations yield only
approximations, but the arising error can be made at least as small as the
The lecture explains the matrix representation, the organisation of the
operations and underlines the black-box character of the method.
Furthermore, applications are described which are usually considered
to be impossible for large scale matrices: computation of functions of
matrices and solution of matrix equations (Lyapunov etc.).