Hierarchical matrix: Difference between revisions

Revision as of 19:23, 16 June 2017

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<ref name="BEHA03">{{cite journal|last=Bebendorf|first=Mario|last2=Hackbusch|first2=Wolfgang|date=2003|title=Existence of H-matrix approximants to the inverse FE-matrix of elliptic operators with <math>L^\infty</math>-coefficients|journal=Num. Math.|volume=95|pages=1&ndash;28}}</ref>

<ref name="BO10">{{cite journal|last=Börm|first=Steffen|date=2010|title=Approximation of solution operators of elliptic partial differential equations by H- and H²-matrices|journal=Num. Math.|volume=115|pages=165&ndash;193|url=http://dx.doi.org/10.1007/s00211-009-0278-7}}</ref>

,<ref name ="FAMEPR13">{{cite journal|last=Faustmann|first=Markus|last2=Melenk|first2=J.&nbsp;Markus|last3=Praetorius|first3=Dirk|date=2015|title=H-matrix approximability of the inverses of FEM matrices|journal=Num. Math.|volume=131|pages=615&ndash;642|url=http://dx.doi.org/10.1007/s00211-015-0706-9}}</ref>,

a rank proportional to <math>\log(1/\epsilon)^\gamma</math> with a small constant <math>\gamma</math> is sufficient to ensure an

accuracy of <math>\epsilon</math>.