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In a similar way, the [[LU decomposition]]
<ref name="BE07">{{cite journal|last=Bebendorf|first=Mario|date=2007|title=Why finite element discretizations can be factored by triangular hierarchical matrices|journal=SIAM J. Numer. Anal.|volume=45|issue=4|pages=1472–1494|doi=10.1137/060669747}}</ref>
<ref name="GRKRBO09">{{cite journal|last=Grasedyck|first=Lars|last2=Kriemann|first2=Ronald|last3=Le Borne|first3=Sabine|date=2009|title=Domain decomposition based H-LU preconditioning|journal=Numer. Math.|volume=112|issue=4|pages=565–600|doi=10.1007/s00211-009-0218-6|doi-access=free}}</ref>
can be constructed using only recursion and multiplication.
Both operations also require <math>O(n k^2\,\log(n)^2)</math> operations.
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leads to approximations that preserve the rate of convergence of the underlying boundary element method
at a complexity of <math>O(n).</math><ref name="SA00">{{cite journal|last=Sauter|first=Stefan|date=2000|title=Variable order panel clustering|journal=Computing|volume=64|issue=3|pages=223–261|doi=10.1007/s006070050045}}</ref>
<ref name="BOSA05">{{cite journal|last=Börm|first=Steffen|last2=Sauter|first2=Stefan|date=2005|title=BEM with linear complexity for the classical boundary integral operators|journal=Math. Comp.|volume=74|issue=251|pages=1139–1177|doi=10.1090/s0025-5718-04-01733-8|doi-access=free}}</ref>
Arithmetic operations like multiplication, inversion, and Cholesky or LR factorization of H<sup>2</sup>-matrices
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