On the Numerical Rank of the Off-Diagonal Blocks of Schur Complements of Discretized Elliptic PDEs

Authors:
S. Chandrasekaran;P. Dewilde;M. Gu;N. Somasunderam
Affiliations:
shiv@ece.ucsb.edu and naveen@umail.ucsb.edu;p.dewilde@ewi.tudelft.nl;mgu@math.berkeley.edu;-
Venue:
SIAM Journal on Matrix Analysis and Applications
Year:
2010

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Abstract

It is shown that the numerical rank of the off-diagonal blocks of certain Schur complements of matrices that arise from the finite-difference discretization of constant coefficient, elliptic PDEs in two spatial dimensions is bounded by a constant independent of the grid size. Moreover, in three-dimensional problems the Schur complements are shown to have off-diagonal blocks whose numerical rank is a slowly growing function.