Abstract
We introduce some generalized concepts of displacement structure for structured matrices obtained as products and inverses of Toeplitz, Hankel, and Vandermonde matrices. The Toeplitz case has already been studied at some length, and the corresponding matrices have been called near-Toeplitz or Toeplitz-like or Toeplitz-derived. We focus on Hankel- and Vandermonde-like matrices and in particular show how the appropriately defined displacement structure yields fast triangular and orthogonal factorization algorithms for such matrices. The main contribution of this paper is presenting a unified framework rather than obtaining the fastest algorithm for each special matrix.
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