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MiS Preprint

Introduction to Hierarchical Matrices with Applications

Steffen Börm, Lars Grasedyck and Wolfgang Hackbusch


We give a short introduction to methods for the data-sparse approximation of matrices resulting from the discretisation of non-local operators occurring in boundary integral methods, as the inverses of partial differential operators or as solutions of control problems.

The result of the approximation will be so-called hierarchical matrices (or short H-matrices). These matrices form a subset of the set of all matrices and have a data-sparse representation. The essential operations for these matrices (matrix-vector and matrix-matrix multiplication, addition and inversion) can be performed in, up to logarithmic factors, optimal complexity.

We give a review of specialised variants of H-matrices, especially ofH2-matrices, and finally consider applications of the different methods to problems from integral equations, partial differential equations and control theory.

MSC Codes:
65F05, 65F30, 65F50, 65N50
hierarchical matrices, formatted matrix operations, lyapunov equation, riccati equation, fast solvers

Related publications

2003 Repository Open Access
Steffen Börm, Lars Grasedyck and Wolfgang Hackbusch

Introduction to hierarchical matrices with applications

In: Engineering analysis with boundary elements, 27 (2003) 5, pp. 405-422