Solving structured linear systems with large displacement rank

Linear systems with structures such as Toeplitz, Vandermonde or Cauchy-likeness can be solved in operations, where n is the matrix size, α is its displacement rank, and denotes the omission of logarithmic factors. We show that for such matrices, this cost can be reduced to , 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 . We present consequences for Hermite–Padé approximation and bivariate interpolation.