On Functions of quasi Toeplitz matrices
Dario A. Bini, Stefano Massei, Beatrice Meini

TL;DR
This paper studies functions of quasi-Toeplitz matrices, providing conditions for their well-definedness, parametrization, and algorithms for computation, with applications to matrices with Toeplitz and low-rank structures.
Contribution
It introduces a framework for analyzing functions of CQT matrices, including conditions, parametrization, and algorithms for their computation, extending to finite matrices with Toeplitz and low-rank parts.
Findings
Conditions for $f(M)$ to be a CQT matrix
Parametrization of CQT matrices
Algorithms for computing $f(M)$
Abstract
Let be a complex valued continuous function, defined for , such that . Consider the semi-infinite Toeplitz matrix associated with the symbol such that . A quasi-Toeplitz matrix associated with the continuous symbol is a matrix of the form where , , and is called a CQT-matrix. Given a function and a CQT matrix , we provide conditions under which is well defined and is a CQT matrix. Moreover, we introduce a parametrization of CQT matrices and algorithms for the computation of . We treat the case where is assigned in terms of power series and the case where is defined in terms of a Cauchy integral. This analysis is applied also to finite…
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
