Iterative Solution of Large Sparse Systems of Equations

 
 
Springer (Verlag)
  • 2. Auflage
  • |
  • erschienen am 31. Mai 2018
 
  • Buch
  • |
  • Softcover
  • |
  • 536 Seiten
978-3-319-80360-9 (ISBN)
 
In the second edition of this classic monograph, complete with four new chapters and updated references, readers will now have access to content describing and analysing classical and modern methods with emphasis on the algebraic structure of linear iteration, which is usually ignored in other literature. The necessary amount of work increases dramatically with the size of systems, so one has to search for algorithms that most efficiently and accurately solve systems of, e.g., several million equations. The choice of algorithms depends on the special properties the matrices in practice have. An important class of large systems arises from the discretization of partial differential equations. In this case, the matrices are sparse (i.e., they contain mostly zeroes) and well-suited to iterative algorithms. The first edition of this book grew out of a series of lectures given by the author at the Christian-Albrecht University of Kiel to students of mathematics. The second edition includes quite novel approaches.
Paperback
Softcover reprint of the original 2nd ed. 2016
  • Englisch
  • Cham
  • |
  • Schweiz
Springer International Publishing
  • Für Beruf und Forschung
  • Überarbeitete Ausgabe
  • 11 farbige Abbildungen, 15 s/w Abbildungen, 10 farbige Tabellen
  • |
  • 10 Tables, color; 11 Illustrations, color; 15 Illustrations, black and white; XXIII, 509 p. 26 illus., 11 illus. in color.
  • Höhe: 236 mm
  • |
  • Breite: 159 mm
  • |
  • Dicke: 32 mm
  • 810 gr
978-3-319-80360-9 (9783319803609)
10.1007/978-3-319-28483-5
weitere Ausgaben werden ermittelt
Wolfgang Hackbusch is a Professor in the Scientific Computing department at Max Planck Institute for Mathematics in the Sciences. His research areas include numerical treatment of partial differential equations, numerical treatment of integral equations, and hierarchical matrices.
Part I: Linear Iterations.- Introduction.- Iterative Methods.- Classical Linear Iterations in the Positive Definite Case.- Analysis of Classical Iterations Under Special Structural Conditions.- Algebra of Linear Iterations.- Analysis of Positive Definite Iterations.- Generation of Iterations. Part II: Semi-Iterations and Krylov Methods.- Semi-Iterative Methods.- Gradient Methods.- Conjugate Gradient Methods and Generalizations.- Part III: Special Iterations.- Multigrid Iterations.- Domain Decomposition and Subspace Methods.- H-LU Iteration.- Tensor-based Methods.- Appendices.
In the second edition of this classic monograph, complete with four new chapters and updated references, readers will now have access to content describing and analysing classical and modern methods with emphasis on the algebraic structure of linear iteration, which is usually ignored in other literature.
The necessary amount of work increases dramatically with the size of systems, so one has to search for algorithms that most efficiently and accurately solve systems of, e.g., several million equations. The choice of algorithms depends on the special properties the matrices in practice have. An important class of large systems arises from the discretization of partial differential equations. In this case, the matrices are sparse (i.e., they contain mostly zeroes) and well-suited to iterative algorithms.
The first edition of this book grew out of a series of lectures given by the author at the Christian-Albrecht University of Kiel to students of mathematics. The second edition includes quite novel approaches.
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