Approximating the inverse of a symmetric positive definite matrix

AbstractIt is shown for an n × n symmetric positive definite matrix T = (ti, j with negative off-diagonal elements, positive row sums and satisfying certain bounding conditions that its inverse is well approximated, uniformly to order l/n2, by a matrix S = (si, j), where si,j = δi,j/ti,j + 1/t.., δi,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