The spectral norm of a Horadam circulant matrix

TL;DR

This paper investigates the spectral norm of circulant matrices constructed from Horadam sequences, extending existing results and providing new insights into their spectral properties.

Contribution

It offers a novel analysis of the spectral norm for circulant matrices derived from Horadam sequences, complementing prior research.

Findings

Derived explicit formulas for the spectral norm

Extended known results to a broader class of sequences

Provided bounds and asymptotic behavior of the spectral norm

Abstract

Let $a$, $b$, $p$, $q$ be integers and~$(h_n)$ defined by $h_0=a$, $h_1=b$, $h_n=ph_{n-1}+qh_{n-2}$, $n=2,3,\dots$. Complementing to certain previously known results, we study the spectral norm of the circulant matrix corresponding to $h_0,\dots,h_{n-1}$.