Iterative Solution of Large Sparse Systems of Equations

Wolfgang Hackbusch (Autor)

Buch | Hardcover

XXIII, 509 Seiten

2016 | 2nd ed. 2016
Springer International Publishing (Verlag)
978-3-319-28481-1 (ISBN)

Artikel merken

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.

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

Erscheinungsdatum	12.07.2016
Reihe/Serie	Applied Mathematical Sciences ; 95
Zusatzinfo	XXIII, 509 p. 26 illus., 11 illus. in color.
Verlagsort	Cham
Sprache	englisch
Maße	155 x 235 mm
Gewicht	962 g
Themenwelt	Mathematik / Informatik ► Mathematik ► Algebra
	Mathematik / Informatik ► Mathematik ► Analysis
	Mathematik / Informatik ► Mathematik ► Wahrscheinlichkeit / Kombinatorik
Schlagworte	Analysis • Gleichungen • Iteration • iterative methods • iterative solution methods • Linear and Multilinear Algebras, Matrix Theory • Linear Iterations • mathematics and statistics • matrices • matrix theory • Multigrid Method • Nonlinear Equations • Numerical analysis • Partial differential equations • Tensor-based Methods
ISBN-10	3-319-28481-9 / 3319284819
ISBN-13	978-3-319-28481-1 / 9783319284811
Zustand	Neuware