Inversion of the Toeplitz-block Toeplitz matrices and the structure of the corresponding inverse matrices

Abstract

The results on the inversion of convolution operators and Toeplitz matrices in the 1-D (one dimensional) case are classical and have numerous applications. We consider a 2-D case of Toeplitz-block Toeplitz matrices, describe a minimal information, which is necessary to recover the inverse matrices, and give a complete characterisation of the inverse matrices.

The ideas and proofs given in this paper are easily modified for the case of convolution operators (see some results on the inversion of the 2-D convolution operators in arXiv:1701.08559, where we mostly omit the proofs). However, the results obtained for the Toeplitz-block Toeplitz matrices are more complete

References in corpus (2)

• General solution of the Poisson equation for Quasi-Birth-and-Death processes
• Estimating the Norms of Random Circulant and Toeplitz Matrices and Their Inverses

Cited by in corpus (1)

• On the inversion of the block double-structured and of the triple-structured Toeplitz matrices and on the corresponding reflection coefficients