Overview

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 hierarchicalmatrices is of interest to scientists in computational mathematics, physics, chemistry and engineering.

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9783662568941

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Reviews

Every line of the book reflects that the author is the leading expert for hierarchical matrices. ... Hierarchical matrices: algorithms and analysis is without a doubt a beautiful, comprehensive introduction to hierarchical matrices that can serve as both a graduate level textbook and a valuable resource for future research. (Thomas Mach, Mathematical Reviews, April, 2017) The book `Hierarchical matrices: algorithms and analysis' is a self-contained monograph which presents an efficient possibility to handle the numerical treatment of fully populated large scale matrices appearing in scientific computations, and therefore it is of interest to scientists in computational mathematics, physics, chemistry and engineering. (Constantin Popa, zbMATH 1336.65041, 2016)

Author Information

The author is a very well-known author of Springer, working in the field of numerical mathematics for partial differential equations and integral equations. He has published numerous books in the SSCM series, e.g., about the multi-grid method, about the numerical analysis of elliptic pdes, about iterative solution of large systems of equation, and a book in German about the technique of hierarchical matrices. Hackbusch is member of the editorial board of Springer' s book series ""Advances in Numerical Mathematics"", ""The International Cryogenics Monograph Series"" and has now joined as new member of the editorial board of ""Springer Series of Computational Mathematics"".

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