Hierarchical Matrices: Algorithms and Analysis by Wolfgang Hackbusch
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.
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Numerical Analysis for Elliptic Optimal Control Problems
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Introduction to Shape Optimization
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Numerical Methods for Two-phase Incompressible Flows
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Time-Domain Finite Element Methods for Maxwell's Equations in Metamaterials
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Spectral Methods
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The Graduate Student's Guide to Numerical Analysis '98
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The Linearization Method for Constrained Optimization
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Hilbert Space Splittings and Iterative Methods
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The Concept of Stability in Numerical Mathematics
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Monotone Discretizations for Elliptic Second Order Partial Differential Equations
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Boundary Element Methods
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History of Continued Fractions and Padé Approximants
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Method of Difference Potentials and Its Applications
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Newton Methods for Nonlinear Problems
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High Order Difference Methods for Time Dependent PDE
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Logarithmic Norms
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Minimization Methods for Non-Differentiable Functions
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Numerical Toolbox for Verified Computing I
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Mixed and Hybrid Finite Element Methods
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Solving Elliptic Problems Using ELLPACK
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Discrete Iterations
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Numerical Techniques for Stochastic Optimization
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Numerical Continuation Methods
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Krylov Methods for Nonsymmetric Linear Systems
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Progress in Approximation Theory
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Sequence Transformations
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Nonlinear Approximation Theory
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Moduli of Smoothness
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Numerical Methods Based on Sinc and Analytic Functions
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Krylov Subspace Methods for Linear Systems
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Advanced Boundary Element Methods
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Retarded Potentials and Time Domain Boundary Integral Equations
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Numerical Modeling in Materials Science and Engineering
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Robust Numerical Methods for Singularly Perturbed Differential Equations
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Finite Element Methods for Incompressible Flow Problems
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Solving Ordinary Differential Equations I
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Solving Ordinary Differential Equations II
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Tensor Spaces and Numerical Tensor Calculus
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Matrix Iterative Analysis
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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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Hierarchische Matrizen
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Integral Equations
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Iterative Solution of Large Sparse Systems of 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
“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)
| SKU | Unavailable |
| ISBN 13 | 9783662568941 |
| ISBN 10 | 3662568942 |
| Title | Hierarchical Matrices: Algorithms and Analysis |
| Author | Wolfgang Hackbusch |
| Series | Springer Series In Computational Mathematics |
| Condition | Unavailable |
| Binding Type | Paperback |
| Publisher | Springer |
| Year published | 2019-03-14 |
| Number of pages | 511 |
| Cover note | Book picture is for illustrative purposes only, actual binding, cover or edition may vary. |
| Note | Unavailable |