Solving structured linear systems with large displacement rank

Linear systems with structures such as Toeplitz, Vandermonde or Cauchy-likeness can be solved in O (̃α2n) operations, where n is the matrix size, α is its displacement rank, and O ̃ denotes the omission of logarithmic factors. We show that for such matrices, this cost can be reduced to O (̃αω−1n), where ω is a feasible exponent for matrix multiplication over the base field. The best known estimate for ω is ω < 2.38, resulting in costs of order O (̃α1.38n). We present consequences for Hermite-Padé approximation and bivariate interpolation.