Efficient inversion formulas for Toeplitz-plus-Hankel matrices using trigonometric transformations (Q2784767)

The authors continue their investigations started in [Linear Algebra Appl. 275-276, 225-248 (1998; Zbl 0935.65040), and 284, 157-175 (1998; Zbl 0938.65073)] where they gave representations of real Toeplitz and Toeplitz-Hankel matrices with trigonometric transforms and representations of inverses of complex Toeplitz-plus-Hankel matrices using complex discrete Fourier transforms. They present further development of their approach for Toeplitz-plus-Hankel matrices and more general Bézoutians, the main result being a possibility to reduce the order of operations needed to calculate the product of a column with an \(n\times n\)-matrix. Namely, to calculate this product they need only 6 transformations and \(O(n)\)-operations, which is better than even in the more studied case of inverse Toeplitz or Hankel operations.NEWLINENEWLINEFor the entire collection see [Zbl 0972.00035].