Solving structured linear systems with large displacement rank

Authors:
Alin Bostan;Claude-Pierre Jeannerod;Éric Schost
Affiliations:
Algorithms Project, INRIA Paris-Rocquencourt, 78153 Le Chesnay Cedex, France;Arénaire Project, INRIA Rhônes-Alpes, Laboratoire LIP (CNRS, ENSL, INRIA, UCBL), ENS Lyon, France;Computer Science Department, The University of Western Ontario, London, Ontario, Canada
Venue:
Theoretical Computer Science
Year:
2008

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Abstract

Linear systems with structures such as Toeplitz, Vandermonde or Cauchy-likeness can be solved in O@?(@a^2n) operations, where n is the matrix size, @a 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@?(@a^@w^-^1n), where @w is a feasible exponent for matrix multiplication over the base field. The best known estimate for @w is @w