  We propose a new O(n)-space implementation of the GKO-Cauchy algorithm for
the solution of linear systems with Cauchy-like matrix. Despite its slightly
higher computational cost, this new algorithm makes a more efficient use of the
processor cache memory. Thus, for matrices of size larger than about 500-1000,
it outperforms the existing algorithms.
  We present an applicative case of Cauchy-like matrices with
non-reconstructible main diagonal. In this special instance, the O(n) space
algorithms can be adapted nicely to provide an efficient implementation of
basic linear algebra operations in terms of the low displacement-rank
generators.
