Cyclic displacements and decompositions of inverse matrices for CUPL Toeplitz matrices

In this paper, we deal mainly with a class of CUPL Toeplitz matrices [32] without Toeplitz structure, which are “close” to the Toeplitz matrices in the sense that their (1,1)-cyclic displacements coincide with φ-cyclic displacement of some Toeplitz matrices. By constructing the corresponding displacement of the matrices, we derive the formulas on representation of the inverses of the CUPL Toeplitz matrices in the form of sums of products of factor row first-plus-last right circulants. Furthermore, the inverses of the CUPL Hankel matrices can be also obtained, which benefits from the relation between the CUPL Toeplitz matrices and the CUPL Hankel matrices.