@article{BoJeSc08, author = {Bostan, Alin and Jeannerod, Claude-Pierre and Schost, \'Eric}, title = {Solving structured linear systems with large displacement rank}, journal = {Theoretical Computer Science}, volume = {407}, number = {1-3}, year = {2008}, pages = {155--181}, doi = {http://dx.doi.org/10.1016/j.tcs.2008.05.014}, publisher = {Elsevier Science Publishers Ltd.}, address = {Essex, UK}, abstract = {Linear systems with structures such as Toeplitz-, Vander\-mon de- or Cauchy-likeness can be solved in $\tilde O (\alpha^2 n)$ operations, wher e $n$ is the matrix size, $\alpha$ is its displacement rank, and $\tilde O (\,)$ denotes the omission of logarithmic factors. We show that for such matrices, th is cost can be reduced to $\tilde O (\alpha^{\omega-1} n)$, where $\omega$ is a feasible exponent for matrix multiplication over the base field. The best known estimate for $\omega$ is $\omega < 2.38$, resulting in costs of order $\tilde O (\alpha^{1.38} n)$. We present consequences for Hermite-Pad\'e approximation an d bivariate interpolation.}, }