Hierarchical Matrices: Algorithms and Analysis by Wolfgang Hackbusch (English) P

Description: Hierarchical Matrices: Algorithms and Analysis by Wolfgang Hackbusch The new technique enables not only the solution of linear systems but also the approximation of matrix functions, e.g., the matrix exponential. 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. FORMAT Paperback LANGUAGE English CONDITION Brand New Publisher Description 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. Back Cover 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. Author Biography 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". Table of 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. Review "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) Review Quote "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) Feature Matrix algorithms of almost linear cost Application to matrix equations and matrix functions Self-contained contents by means of five appendices Details ISBN3662568942 Author Wolfgang Hackbusch Language English ISBN-10 3662568942 ISBN-13 9783662568941 Format Paperback Pages 511 Imprint Springer-Verlag Berlin and Heidelberg GmbH & Co. K Place of Publication Berlin Country of Publication Germany DEWEY 512.9434 Illustrations 27 Illustrations, color; 60 Illustrations, black and white; XXV, 511 p. 87 illus., 27 illus. in color. Year 2019 Publication Date 2019-03-14 Series Number 49 UK Release Date 2019-03-14 Edited by Marc Schleunitz Birth 1962 Affiliation Stanford University School of Medicine Position Contributor Qualifications PhD Publisher Springer-Verlag Berlin and Heidelberg GmbH & Co. KG Edition Description Softcover reprint of the original 1st ed. 2015 Series Springer Series in Computational Mathematics Alternative 9783662473238 Audience Professional & Vocational We've got this At The Nile, if you're looking for it, we've got it. With fast shipping, low prices, friendly service and well over a million items - you're bound to find what you want, at a price you'll love! TheNile_Item_ID:127853694;

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