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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.
Algebra --- Partial differential equations --- Numerical analysis --- Computer science --- differentiaalvergelijkingen --- algebra --- matrices --- algoritmen --- numerieke analyse --- Mathematics. --- Matrices --- Algebra. --- Integral equations. --- Differential equations, Partial. --- Algorithms. --- Numerical analysis. --- Mathématiques --- Algèbre --- Équations intégrales --- Équations aux dérivées partielles --- Algorithmes --- Analyse numérique --- Data processing. --- Informatique
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Computational methods in engineering boundary value problems
Numerical analysis --- Computer. Automation --- Boundary value problems --- Mathematical physics. --- Numerical solutions. --- Numerical solutions --- Differential equations, Partial --- Initial value problems --- Analyse numérique --- Équations aux dérivées partielles --- Mathématiques de l'ingénieur --- Problèmes aux valeurs initiales
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