The Resource Hierarchical Matrices: Algorithms and Analysis, by Wolfgang Hackbusch, (electronic resource)

Hierarchical Matrices: Algorithms and Analysis, by Wolfgang Hackbusch, (electronic resource)

Label
Hierarchical Matrices: Algorithms and Analysis
Title
Hierarchical Matrices: Algorithms and Analysis
Statement of responsibility
by Wolfgang Hackbusch
Creator
Contributor
Author
Provider
Subject
Language
eng
Summary
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
Member of
http://library.link/vocab/creatorName
Hackbusch, Wolfgang
Image bit depth
0
LC call number
QA297-299.4
Literary form
non fiction
http://library.link/vocab/relatedWorkOrContributorName
SpringerLink
Series statement
Springer Series in Computational Mathematics,
Series volume
49
http://library.link/vocab/subjectName
  • Mathematics
  • Matrix theory
  • Algebra
  • Integral equations
  • Partial differential equations
  • Algorithms
  • Numerical analysis
  • Mathematics
  • Numerical Analysis
  • Algorithms
  • Partial Differential Equations
  • Integral Equations
  • Linear and Multilinear Algebras, Matrix Theory
Label
Hierarchical Matrices: Algorithms and Analysis, by Wolfgang Hackbusch, (electronic resource)
Instantiates
Publication
Antecedent source
mixed
Carrier category
online resource
Carrier category code
cr
Carrier MARC source
rdacarrier
Color
not applicable
Content category
text
Content type code
txt
Content type MARC source
rdacontent
Contents
Preface -- Part I: Introductory and Preparatory Topics -- 1. Introduction -- 2. Rank-r Matrices -- 3. Introductory Example -- 4. Separable Expansions and Low-Rank Matrices -- 5. Matrix Partition -- Part II: H-Matrices and Their Arithmetic -- 6. Definition and Properties of Hierarchical Matrices.- 7. Formatted Matrix Operations for Hierarchical Matrices -- 8. H2-Matrices -- 9. Miscellaneous Supplements -- Part III: Applications.- 10. Applications to Discretised Integral Operators -- 11. Applications to Finite Element Matrices -- 12. Inversion with Partial Evaluation -- 13. Eigenvalue Problems -- 14. Matrix Functions -- 15. Matrix Equations -- 16. Tensor Spaces.- Part IV: Appendices -- A. Graphs and Trees -- B. Polynomials -- C. Linear Algebra and Functional Analysis -- D. Sinc Functions and Exponential Sums -- E. Asymptotically Smooth Functions -- References -- Index
Dimensions
unknown
Edition
1st ed. 2015.
Extent
XXV, 511 p. 87 illus., 27 illus. in color.
File format
multiple file formats
Form of item
electronic
Isbn
9783662473245
Level of compression
uncompressed
Media category
computer
Media MARC source
rdamedia
Media type code
c
Other control number
10.1007/978-3-662-47324-5
Other physical details
online resource.
Quality assurance targets
absent
Reformatting quality
access
Specific material designation
remote
System control number
(DE-He213)978-3-662-47324-5
Label
Hierarchical Matrices: Algorithms and Analysis, by Wolfgang Hackbusch, (electronic resource)
Publication
Antecedent source
mixed
Carrier category
online resource
Carrier category code
cr
Carrier MARC source
rdacarrier
Color
not applicable
Content category
text
Content type code
txt
Content type MARC source
rdacontent
Contents
Preface -- Part I: Introductory and Preparatory Topics -- 1. Introduction -- 2. Rank-r Matrices -- 3. Introductory Example -- 4. Separable Expansions and Low-Rank Matrices -- 5. Matrix Partition -- Part II: H-Matrices and Their Arithmetic -- 6. Definition and Properties of Hierarchical Matrices.- 7. Formatted Matrix Operations for Hierarchical Matrices -- 8. H2-Matrices -- 9. Miscellaneous Supplements -- Part III: Applications.- 10. Applications to Discretised Integral Operators -- 11. Applications to Finite Element Matrices -- 12. Inversion with Partial Evaluation -- 13. Eigenvalue Problems -- 14. Matrix Functions -- 15. Matrix Equations -- 16. Tensor Spaces.- Part IV: Appendices -- A. Graphs and Trees -- B. Polynomials -- C. Linear Algebra and Functional Analysis -- D. Sinc Functions and Exponential Sums -- E. Asymptotically Smooth Functions -- References -- Index
Dimensions
unknown
Edition
1st ed. 2015.
Extent
XXV, 511 p. 87 illus., 27 illus. in color.
File format
multiple file formats
Form of item
electronic
Isbn
9783662473245
Level of compression
uncompressed
Media category
computer
Media MARC source
rdamedia
Media type code
c
Other control number
10.1007/978-3-662-47324-5
Other physical details
online resource.
Quality assurance targets
absent
Reformatting quality
access
Specific material designation
remote
System control number
(DE-He213)978-3-662-47324-5

Library Locations

  • African Studies LibraryBorrow it
    771 Commonwealth Avenue, 6th Floor, Boston, MA, 02215, US
    42.350723 -71.108227
  • Alumni Medical LibraryBorrow it
    72 East Concord Street, Boston, MA, 02118, US
    42.336388 -71.072393
  • Astronomy LibraryBorrow it
    725 Commonwealth Avenue, 6th Floor, Boston, MA, 02445, US
    42.350259 -71.105717
  • Fineman and Pappas Law LibrariesBorrow it
    765 Commonwealth Avenue, Boston, MA, 02215, US
    42.350979 -71.107023
  • Frederick S. Pardee Management LibraryBorrow it
    595 Commonwealth Avenue, Boston, MA, 02215, US
    42.349626 -71.099547
  • Howard Gotlieb Archival Research CenterBorrow it
    771 Commonwealth Avenue, 5th Floor, Boston, MA, 02215, US
    42.350723 -71.108227
  • Mugar Memorial LibraryBorrow it
    771 Commonwealth Avenue, Boston, MA, 02215, US
    42.350723 -71.108227
  • Music LibraryBorrow it
    771 Commonwealth Avenue, 2nd Floor, Boston, MA, 02215, US
    42.350723 -71.108227
  • Pikering Educational Resources LibraryBorrow it
    2 Silber Way, Boston, MA, 02215, US
    42.349804 -71.101425
  • School of Theology LibraryBorrow it
    745 Commonwealth Avenue, 2nd Floor, Boston, MA, 02215, US
    42.350494 -71.107235
  • Science & Engineering LibraryBorrow it
    38 Cummington Mall, Boston, MA, 02215, US
    42.348472 -71.102257
  • Stone Science LibraryBorrow it
    675 Commonwealth Avenue, Boston, MA, 02445, US
    42.350103 -71.103784
Processing Feedback ...