Springer Series in Computational Mathematics

Hierarchical Matrices: Algorithms and Analysis

Authors: Hackbusch, Wolfgang

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  • Matrix algorithms of almost linear cost
  • Application to matrix equations and matrix functions
  • Self-contained contents by means of five appendices
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eBook $119.00
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  • ISBN 978-3-662-47324-5
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Hardcover $159.99
price for USA in USD
  • ISBN 978-3-662-47323-8
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Softcover $159.99
price for USA in USD
  • Unpublished eBooks cannot be pre-ordered in advance.
  • Due: February 1, 2017
  • ISBN 978-3-662-56894-1
  • Free shipping for individuals worldwide
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 hierarchical matrices is of interest to scientists in computational mathematics, physics, chemistry and engineering.

About the authors

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".

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)


Table of contents (16 chapters)

Buy this book

eBook $119.00
price for USA in USD (gross)
  • ISBN 978-3-662-47324-5
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $159.99
price for USA in USD
  • ISBN 978-3-662-47323-8
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Softcover $159.99
price for USA in USD
  • Unpublished eBooks cannot be pre-ordered in advance.
  • Due: February 1, 2017
  • ISBN 978-3-662-56894-1
  • Free shipping for individuals worldwide
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Bibliographic Information

Bibliographic Information
Book Title
Hierarchical Matrices: Algorithms and Analysis
Authors
Series Title
Springer Series in Computational Mathematics
Series Volume
49
Copyright
2015
Publisher
Springer-Verlag Berlin Heidelberg
Copyright Holder
Springer-Verlag Berlin Heidelberg
eBook ISBN
978-3-662-47324-5
DOI
10.1007/978-3-662-47324-5
Hardcover ISBN
978-3-662-47323-8
Softcover ISBN
978-3-662-56894-1
Series ISSN
0179-3632
Edition Number
1
Number of Pages
XXV, 511
Number of Illustrations
60 b/w illustrations, 27 illustrations in colour
Topics