Iterative Solution of Large Sparse Systems of Equations by Wolfgang Hackbusch
C. F. GauS in a letter from Dec. 26, 1823 to Gerling: 3c empfe le 3 nen biegen IDlobu9 aur 9tac a mung. ec werlic werben eie ie wieber bi reet eliminiren, wenigftens nic t, wenn eie me r als 2 Unbefannte aben.: Da9 inbirecte 93erfa ren 109st sic alb im ec lafe ausfii ren, ober man fann wo renb be9gelben an anbere: Dinge benfen. CO F. GauS: Werke vol. 9, Gottingen, p. 280, 1903] What difference exists between solving large and small systems of equations? The standard methods well-known to any student oflinear algebra are appli cable to all systems, whether large or small. The necessary amount of work, however, increases dramatically with the size, so one has to search for algo rithms that most efficiently and accurately solve systems of 1000, 10,000, or even one 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 discretisation of partial differential equations. In this case, the matrices are sparse (i. e., they contain mostly zeros) and well-suited to iterative algorithms. Because of the background in partial differential equa tions, this book is closely connected with the author's Theory and Numerical Treatment of Elliptic Differential Equations, whose English translation has also been published by Springer-Verlag. This book grew out of a series of lectures given by the author at the Christian-Albrecht University of Kiel to students of mathematics.-
A Practical Guide to Splines
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Fractional Differential Equations
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Partial Differential Equations II
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Elliptic Functions and Applications
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Dynamics: Numerical Explorations
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Averaging for Nonlinear Dynamics with Applications and Numerical Bifurcations
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Direct and Inverse Scattering for the Matrix Schrodinger Equation
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Imperfect Bifurcation in Structures and Materials
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Synchronization in Infinite-Dimensional Deterministic and Stochastic Systems
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Exact and Heuristic Methods in Combinatorial Optimization
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Optimal Control of Partial Differential Equations
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Applications of Percolation Theory
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Falling Liquid Films
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Nonlinear Filtering and Optimal Phase Tracking
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Mathematical Problems in Image Processing
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Fluid Dynamics of Viscoelastic Liquids
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An Introduction to Theory and Applications of Stationary Variational-Hemivariational Inequalities
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The Geometry of Minkowski Spacetime
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Lectures on Variational Analysis
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Level Set Methods and Dynamic Implicit Surfaces
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Brownian Dynamics at Boundaries and Interfaces
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Adaptive Moving Mesh Methods
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Nonlinear Functional Analysis with Applications to Combustion Theory
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Dynamical Systems and Chaos
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Bifurcation Theory
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Nonlinear Dispersive Equations
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Infinite-Dimensional Dynamical Systems in Mechanics and Physics
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Transient Chaos
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Chaos, Fractals, and Noise
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Mathematical Problems from Combustion Theory
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Linear Integral Equations
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Singularities and Groups in Bifurcation Theory
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Normal Forms, Melnikov Functions and Bifurcations of Limit Cycles
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Applied Functional Analysis
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Robust Control Theory in Hilbert Space
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Invariant Manifolds and Fibrations for Perturbed Nonlinear Schroedinger Equations
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Normally Hyperbolic Invariant Manifolds in Dynamical Systems
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Prandtl-Essentials of Fluid Mechanics
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The Concept of Stability in Numerical Mathematics
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Multigrid Methods V
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Theorie und Numerik elliptischer Differentialgleichungen
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Efficient Solutions of Elliptic Systems
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Numerical Treatment of Coupled Systems
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Boundary Elements: Implementation and Analysis of Advanced Algorithms
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Hierarchical Matrices: Algorithms and Analysis
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Hierarchische Matrizen
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Integral Equations
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Tensor Spaces and Numerical Tensor Calculus
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Elliptic Differential Equations
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Multi-Grid Methods and Applications
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Iterative Lösung großer schwachbesetzter Gleichungssysteme
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Robust Multi-Grid Methods
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Integralgleichungen
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Numerical Techniques for Boundary Element Methods
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Numerical Treatment of the Navier-Stokes Equations
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Fast Solvers for Flow Problems
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Incomplete Decomposition (ILU) — Algorithms, Theory, and Applications
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Multigrid Methods II
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.
| SKU | Unavailable |
| ISBN 13 | 9783319284811 |
| ISBN 10 | 3319284819 |
| Title | Iterative Solution of Large Sparse Systems of Equations |
| Author | Wolfgang Hackbusch |
| Series | Applied Mathematical Sciences |
| Condition | Unavailable |
| Binding Type | Hardback |
| Publisher | Springer International Publishing AG |
| Year published | 2016-07-01 |
| Number of pages | 509 |
| Cover note | Book picture is for illustrative purposes only, actual binding, cover or edition may vary. |
| Note | Unavailable |