Solving toeplitz- and vandermonde-like linear systems with large displacement rank

Linear systems with structures such as Toeplitz-, Vandermonde- or Cauchy-likeness can be solved in O˜(α2 n) operations, where n is the matrix size, α is its displacement rank, and O˜ denotes the omission of logarithmic factors. We show that for Toeplitz-like and Vandermonde-like matrices, this cost can be reduced to O˜(αω−1 n), 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

• Type: Conference
• Year: 2007
• Where: ISSAC
• Authors: Alin Bostan, Claude-Pierre Jeannerod, Éric Schost
• Keywords: Displacement Rank, ISSAC 2007, Linear Systems, Matrix Size