Abstract
Fast algorithms for computing the product with a vector are presented for a number of classes of matrices whose properties relate to the properties of Toeplitz, Vandermonde, or Cauchy matrices (these matrices are defined using the concept of displacement of a matrix) and also for their inverses. All the actions which are not dependent upon the coordinates of the input vector are singled out in a separate preprocessing stage. The proposed algorithms are based on new representations of these matrices, involving factor circulants.
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