In recent papers, the connection between Toeplitz-like matrices, Vandermonde matrices, and Cauchy matrices is analyzed. Especially every Toeplitz matrix can be written as a Cauchy matrix by means of the Fourier or Sine transform. This gives rise to the formulation of new stable direct solvers for linear Toeplitz systems. Also for iterative methods the transformation of a Toeplitz matrix into a Cauchy matrix allows a new view on fast transform based preconditioning for Toeplitz-like matrices. In this paper we will display some theoretical and practical applications of this new development.
Thomas K. Huckle,
"Cauchy matrices and iterative methods for Toeplitz matrices", Proc. SPIE 2563, Advanced Signal Processing Algorithms, (7 June 1995); doi: 10.1117/12.211405; https://doi.org/10.1117/12.211405