The authors extend some recent results of Di Fiore and Zellini [Linear Algebra Appl., to appear], obtaining new classes of formulas for the displacement operator-based decomposition of matrices. It is shown how an arbitrary matrix can be expressed as the sum of products of matrices belonging to matrix algebras associated with certain versions of sine and cosine transforms. Applications to the representation of the inverse of a Toeplitz and a Toeplitz plus Hankel matrix, with and without symmetry, are presented. Implications on the computation of the product of these matrices by a vector are discussed.
Bozzo, E., DI FIORE, C. (1995). On the use of certain matrix algebras associated with discrete trigonometric transforms in matrix displacement decomposition. SIAM JOURNAL ON MATRIX ANALYSIS AND APPLICATIONS, 16(1), 312-326.
On the use of certain matrix algebras associated with discrete trigonometric transforms in matrix displacement decomposition
DI FIORE, CARMINE
1995-01-01
Abstract
The authors extend some recent results of Di Fiore and Zellini [Linear Algebra Appl., to appear], obtaining new classes of formulas for the displacement operator-based decomposition of matrices. It is shown how an arbitrary matrix can be expressed as the sum of products of matrices belonging to matrix algebras associated with certain versions of sine and cosine transforms. Applications to the representation of the inverse of a Toeplitz and a Toeplitz plus Hankel matrix, with and without symmetry, are presented. Implications on the computation of the product of these matrices by a vector are discussed.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
