APPROXIMATING THE INVERSE OF A POSITIVE DEFINITE MATRIX
by Gordon Simons and Yi-Ching Yao
Abstract
It is shown for an n by n positive definite matrix T = (t(i,j)) with
negative off-diagonal elements and satisfying certain modest bounding
conditions that its inverse is well approximated, uniformly to order
1/n^2, by a matrix S = (s(i,j)), where s(i,j) = delta(i,j)/t(i,i)+1/t..,
delta(i,j) being the Kronecker delta function, and t.. being the sum of
the elements of T. An explicit bound on the approximation error is
provided.