Riordan arrays and the LDU decomposition of symmetric Toeplitz plus Hankel matrices
Paul Barry, Aoife Hennessy
TL;DR
This paper explores the use of Riordan arrays to derive the LDU decomposition of symmetric Toeplitz plus Hankel matrices, providing explicit formulas and analyzing related sequences.
Contribution
It introduces a novel application of Riordan arrays to decompose symmetric Toeplitz plus Hankel matrices and determines their generating functions and Hankel transforms.
Findings
LDU decomposition formulas for specific matrices
Explicit generating functions for associated sequences
Hankel transforms of related sequences
Abstract
We examine a result of Basor and Ehrhardt concerning Hankel and Toeplitz plus Hankel matrices, within the context of the Riordan group of lower-triangular matrices. This allows us to determine the LDU decomposition of certain symmetric Toeplitz plus Hankel matrices. We also determine the generating functions and Hankel transforms of associated sequences.
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.
Taxonomy
TopicsAdvanced Combinatorial Mathematics · graph theory and CDMA systems · Mathematical functions and polynomials