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.