Properties of the Inverse of the Gaussian Matrix

Abstract

The Gaussian matrix is a symmetric Toeplitz matrix and in addition the elements in its first row form a pattern. This enables a specific formula to be obtained, in the nonsingular case, for the elements in the first row of the inverse. Recurrence formulae are then obtained which enable this inverse to be obtained in $\frac{1} {2}n^2 $ flops, as against $2n^2 $ flops, for a general symmetric Toeplitz matrix using the Trench algorithm.