Overview
- Matrix algorithms of almost linear cost
- Application to matrix equations and matrix functions
- Self-contained contents by means of five appendices
- Includes supplementary material: sn.pub/extras
Part of the book series: Springer Series in Computational Mathematics (SSCM, volume 49)
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Table of contents (16 chapters)
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Front Matter
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Introductory and Preparatory Topics
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Front Matter
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$$\mathcal{H}$$ -Matrices and Their Arithmetic
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Front Matter
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<InlineEquation ID="IEq1"><EquationSource Format="TEX"><![CDATA[$$\mathcal{H}$$]]></EquationSource></InlineEquation>-Matrices and Their Arithmetic
Keywords
About this book
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.
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 populatedlarge 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)
Authors and Affiliations
About the author
Bibliographic Information
Book Title: Hierarchical Matrices: Algorithms and Analysis
Authors: Wolfgang Hackbusch
Series Title: Springer Series in Computational Mathematics
DOI: https://doi.org/10.1007/978-3-662-47324-5
Publisher: Springer Berlin, Heidelberg
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: Springer-Verlag Berlin Heidelberg 2015
Hardcover ISBN: 978-3-662-47323-8Published: 21 December 2015
Softcover ISBN: 978-3-662-56894-1Published: 14 March 2019
eBook ISBN: 978-3-662-47324-5Published: 21 December 2015
Series ISSN: 0179-3632
Series E-ISSN: 2198-3712
Edition Number: 1
Number of Pages: XXV, 511
Number of Illustrations: 60 b/w illustrations, 27 illustrations in colour
Topics: Numerical Analysis, Algorithms, Partial Differential Equations, Integral Equations, Linear and Multilinear Algebras, Matrix Theory