Hierarchical Matrices: Algorithms And Analysis (springer Series In Computational Mathematics)
by Wolfgang Hackbusch /
2015 / English / PDF
5 MB Download
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.
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.
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.
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.
