This self-contained monograph presents matrix algorithms and their analysis. The new technique
enables not only the solution of linear systems but also the approximation of matrix functions
e.g. the matrix exponential. Other applications include the solution of matrix equations e.g.
the Lyapunov or Riccati equation. The required mathematical background can be found in the
appendix. The numerical treatment of fully populated large-scale matrices is usually rather
costly. However the technique of hierarchical matrices makes it possible to store matrices and
to perform matrix operations approximately with almost linear cost and a controllable degree of
approximation error. For important classes of matrices the computational cost increases only
logarithmically with the approximation error. The operations provided include the matrix
inversion and LU decomposition. Since large-scale linear algebra problems are standard in
scientific computing the subject of hierarchical matrices is of interest to scientists in
computational mathematics physics chemistry and engineering.
