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IGPM279.pdf October 2007 
TITLE 
Construction of DataSparse H2Matrices by Hierarchical Compression 
AUTHORS 
Steffen Börm 
ABSTRACT 
Discretizing an integral operator by a standard finite element or boundary
element method typically leads to a dense matrix. Since its storage complex
ity grows quadratically with the number of degrees of freedom, the standard
representation of the matrix as a twodimensional array cannot be applied
to large problem sizes.
H2matrix techniques use a multilevel approach to represent the dense
matrix in a more efficient datasparse format. We consider the challenging
task of finding a good multilevel representation of the matrix without relying
on a priori information of its contents.
This paper presents a relatively simple algorithm that can use any of the
popular lowrank approximation schemes (e.g., cross approximation) to find
an “initial guess” and constructs a matching multilevel structure on the fly.
Numerical experiments show that the resulting technique is as fast as competing methods and requires far less storage for large problem dimensions.

KEYWORDS 
hierarchical matrices, datasparse approximation, nonlocal operators
