國立虎尾科技大學 |

Hierarchical Matrices: Algorithms and Analysis

紀錄類型:	書目-語言資料,印刷品 : Monograph/item
正題名/作者:	Hierarchical Matrices: Algorithms and Analysis/ by Wolfgang Hackbusch.
作者:	Hackbusch, Wolfgang.
面頁冊數:	XXV, 511 p. 87 illus., 27 illus. in color.online resource. :
Contained By:	Springer Nature eBook
標題:	Numerical analysis. -
電子資源:	https://doi.org/10.1007/978-3-662-47324-5
ISBN:	9783662473245

Hierarchical Matrices: Algorithms and Analysis
Hackbusch, Wolfgang.

Hierarchical Matrices: Algorithms and Analysis[electronic resource] /by Wolfgang Hackbusch. - 1st ed. 2015. - XXV, 511 p. 87 illus., 27 illus. in color.online resource. - Springer Series in Computational Mathematics,490179-3632 ;. - Springer Series in Computational Mathematics,48.

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.

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.

ISBN: 9783662473245

Standard No.: 10.1007/978-3-662-47324-5doiSubjects--Topical Terms:

527939
Numerical analysis.

LC Class. No.: QA297-299.4

Dewey Class. No.: 518

Hierarchical Matrices: Algorithms and Analysis
LDR:03417nam a22004095i 4500 001 967570
003 DE-He213
005 20200701170847.0
007 cr nn 008mamaa
008 201211s2015 gw | s |||| 0|eng d
020 $a 9783662473245 $9 978-3-662-47324-5
024 7 $a 10.1007/978-3-662-47324-5 $2 doi
035 $a 978-3-662-47324-5
050 4 $a QA297-299.4
072 7 $a PBKS $2 bicssc
072 7 $a MAT021000 $2 bisacsh
072 7 $a PBKS $2 thema
082 0 4 $a 518 $2 23
100 1 $a Hackbusch, Wolfgang. $4 aut $4 http://id.loc.gov/vocabulary/relators/aut $3 890854
245 1 0 $a Hierarchical Matrices: Algorithms and Analysis $h [electronic resource] / $c by Wolfgang Hackbusch.
250 $a 1st ed. 2015.
264 1 $a Berlin, Heidelberg : $b Springer Berlin Heidelberg : $b Imprint: Springer, $c 2015.
300 $a XXV, 511 p. 87 illus., 27 illus. in color. $b online resource.
336 $a text $b txt $2 rdacontent
337 $a computer $b c $2 rdamedia
338 $a online resource $b cr $2 rdacarrier
347 $a text file $b PDF $2 rda
490 1 $a Springer Series in Computational Mathematics, $x 0179-3632 ; $v 49
505 0 $a 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.
520 $a 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.
650 0 $a Numerical analysis. $3 527939
650 0 $a Algorithms. $3 527865
650 0 $a Partial differential equations. $3 1102982
650 0 $a Integral equations. $3 527971
650 0 $a Matrix theory. $3 1023862
650 0 $a Algebra. $2 gtt $3 579870
650 1 4 $a Numerical Analysis. $3 671433
650 2 4 $a Partial Differential Equations. $3 671119
650 2 4 $a Integral Equations. $3 672359
650 2 4 $a Linear and Multilinear Algebras, Matrix Theory. $3 672090
710 2 $a SpringerLink (Online service) $3 593884
773 0 $t Springer Nature eBook
776 0 8 $i Printed edition: $z 9783662473238
776 0 8 $i Printed edition: $z 9783662473252
776 0 8 $i Printed edition: $z 9783662568941
830 0 $a Springer Series in Computational Mathematics, $x 0179-3632 ; $v 48 $3 1258881
856 4 0 $u https://doi.org/10.1007/978-3-662-47324-5
912 $a ZDB-2-SMA
912 $a ZDB-2-SXMS
950 $a Mathematics and Statistics (SpringerNature-11649)
950 $a Mathematics and Statistics (R0) (SpringerNature-43713)