Iterative Solution of Large Sparse Systems of Equations

Wolfgang Hackbusch (Autor)

Buch | Softcover

XXIII, 509 Seiten

2018 | 2. Softcover reprint of the original 2nd ed. 2016
Springer International Publishing (Verlag)
978-3-319-80360-9 (ISBN)

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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	04.05.2019
Reihe/Serie	Applied Mathematical Sciences
Zusatzinfo	XXIII, 509 p. 26 illus., 11 illus. in color.
Verlagsort	Cham
Sprache	englisch
Maße	155 x 235 mm
Gewicht	8015 g
Themenwelt	Mathematik / Informatik ► Mathematik ► Algebra
	Mathematik / Informatik ► Mathematik ► Analysis
	Mathematik / Informatik ► Mathematik ► Wahrscheinlichkeit / Kombinatorik
Schlagworte	Analysis • iterative solution methods • matrices • matrix theory • Multigrid Method • Nonlinear Equations • Partial differential equations • Tensor-based Methods
ISBN-10	3-319-80360-3 / 3319803603
ISBN-13	978-3-319-80360-9 / 9783319803609
Zustand	Neuware