We propose an algorithm for extracting the diagonal of the inverse matrices
arising from electronic structure calculation. The proposed algorithm uses a
hierarchical decomposition of the computational domain. It first constructs
hierarchical Schur complements of the interior points for the blocks of the
domain in a bottom-up pass and then extracts the diagonal entries
efficiently in a top-down pass by exploiting the hierarchical local
dependence of the inverse matrices. The overall cost of our algorithm is
$O(N^3/2)$ for a two dimensional problem with $N$ degrees of freedom.
Numerical results in electronic structure calculation illustrate the
efficiency and accuracy of the proposed algorithm.
@article{1256562822,
author = {Lin, Lin and Lu, Jianfeng and Ying, Lexing and Car, Roberto and E, Weinan},
title = {Fast algorithm for extracting the diagonal of the inverse matrix with
application to the electronic structure analysis of metallic systems},
journal = {Commun. Math. Sci.},
volume = {7},
number = {1},
year = {2009},
pages = { 755-777},
language = {en},
url = {http://dml.mathdoc.fr/item/1256562822}
}
Lin, Lin; Lu, Jianfeng; Ying, Lexing; Car, Roberto; E, Weinan. Fast algorithm for extracting the diagonal of the inverse matrix with
application to the electronic structure analysis of metallic systems. Commun. Math. Sci., Tome 7 (2009) no. 1, pp. 755-777. http://gdmltest.u-ga.fr/item/1256562822/