Multi-grid methods and applications
- W. Hackbusch
- MathematicsSpringer Series in Computational Mathematics
- 1985
This paper presents the Multi-Grid Method of the Second Kind, a method for solving Singular Perturbation Problems and Eigenvalue Problems and Singular Equations of the Two-Grid Iteration.
Singular Integral Equations
- W. Hackbusch
- Mathematics
- 1995
Let the function f be defined on I=[a,b] and, possibly, be singular at an interior point c∈(a,b). Recall that the improper integral was defined by
$$\int\limits_{a}^{b} {f\left( x \right)} dx: =…
A Sparse Matrix Arithmetic Based on H-Matrices. Part I: Introduction to H-Matrices
- W. Hackbusch
- Computer ScienceComputing
- 1999
This paper is the first of a series and is devoted to the first introduction of the H-matrix concept, which allows the exact inversion of tridiagonal matrices.
Iterative Solution of Large Sparse Systems of Equations
- W. Hackbusch
- Computer Science
- 29 November 1993
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…
Tensor Spaces and Numerical Tensor Calculus
- W. Hackbusch
- Mathematics, Computer ScienceSpringer Series in Computational Mathematics
- 24 February 2012
Part I: Algebraic Tensors; Part II: Functional Analysis of Tensor Spaces; Part III: Numerical Treatment.
Construction and Arithmetics of H-Matrices
- L. Grasedyck, W. Hackbusch
- Computer Science, MathematicsComputing
- 1 August 2003
This paper presents a construction of the hierarchical matrix format for standard finite element and boundary element applications for which two criteria, the sparsity and idempotency, are sufficient to give the desired bounds.
Introduction to Hierarchical Matrices with Applications
- S. Börm, L. Grasedyck, W. Hackbusch
- Mathematics, Computer Science
- 1 May 2003
A New Scheme for the Tensor Representation
- W. Hackbusch, S. Kühn
- Computer Science
- 22 October 2009
A truncation algorithm can be implemented which is based on the standard matrix singular value decomposition (SVD) method and is possible to apply standard Linear Algebra tools for performing arithmetical operations and for the computation of data-sparse approximations.
Hierarchical Matrices: Algorithms and Analysis
- W. Hackbusch
- Computer Science, Mathematics
- 14 December 2015
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.,…
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