# An introduction to hierarchical matrices

Wolfgang Hackbusch; Lars Grasedyck; Steffen Börm

Mathematica Bohemica (2002)

- Volume: 127, Issue: 2, page 229-241
- ISSN: 0862-7959

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topHackbusch, Wolfgang, Grasedyck, Lars, and Börm, Steffen. "An introduction to hierarchical matrices." Mathematica Bohemica 127.2 (2002): 229-241. <http://eudml.org/doc/249049>.

@article{Hackbusch2002,

abstract = {We give a short introduction to a method for the data-sparse approximation of matrices resulting from the discretisation of non-local operators occurring in boundary integral methods or as the inverses of partial differential operators. The result of the approximation will be the so-called hierarchical matrices (or short $\mathcal \{H\}$-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.},

author = {Hackbusch, Wolfgang, Grasedyck, Lars, Börm, Steffen},

journal = {Mathematica Bohemica},

keywords = {hierarchical matrices; data-sparse approximations; formatted matrix operations; fast solvers; hierarchical matrices; data-sparse approximations; formatted matrix operations; fast solvers; matrix inversion; boundary integral methods; -matrices; matrix-matrix multiplication; optimal complexity},

language = {eng},

number = {2},

pages = {229-241},

publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},

title = {An introduction to hierarchical matrices},

url = {http://eudml.org/doc/249049},

volume = {127},

year = {2002},

}

TY - JOUR

AU - Hackbusch, Wolfgang

AU - Grasedyck, Lars

AU - Börm, Steffen

TI - An introduction to hierarchical matrices

JO - Mathematica Bohemica

PY - 2002

PB - Institute of Mathematics, Academy of Sciences of the Czech Republic

VL - 127

IS - 2

SP - 229

EP - 241

AB - We give a short introduction to a method for the data-sparse approximation of matrices resulting from the discretisation of non-local operators occurring in boundary integral methods or as the inverses of partial differential operators. The result of the approximation will be the so-called hierarchical matrices (or short $\mathcal {H}$-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.

LA - eng

KW - hierarchical matrices; data-sparse approximations; formatted matrix operations; fast solvers; hierarchical matrices; data-sparse approximations; formatted matrix operations; fast solvers; matrix inversion; boundary integral methods; -matrices; matrix-matrix multiplication; optimal complexity

UR - http://eudml.org/doc/249049

ER -

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