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Hierarchical Matrices: Algorithms and Analysis (Hardcover, 1st ed. 2015)
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Hierarchical Matrices: Algorithms and Analysis (Hardcover, 1st ed. 2015)
Series: Springer Series in Computational Mathematics, 49
Expected to ship within 12 - 19 working days
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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.
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