Transformation techniques for Toeplitz and Toeplitz-plus-Hankel matrices. I. Transformations Original Research Article

Transformations of the form image are investigated that transform Toeplitz and Toeplitz-plus-Hankel matrices into generalized Cauchy matrices. image and image are matrices related to the discrete Fourier transformation or to various real trigonometric transformations. Combining these results with pivoting techniques, in paper II algorithms for Toeplitz and Toeplitz-plus-Hankel systems will be presented that are more stable than classical algorithms.