On the spectral and Frobenius norm of a generalized Fibonacci r-circulant matrix

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    Abstract

    Consider the recursion g0 = a, g1 = b, gn = gn-1 + gn-2, n = 2, 3, . . . . We compute the Frobenius norm of the r-circulant matrix corresponding to g0, . . . , gn-1. We also give three lower bounds (with equality conditions) for the spectral norm of this matrix. For this purpose, we present three ways to estimate the spectral norm from below in general.

    Original languageEnglish
    Pages (from-to)23-36
    Number of pages14
    JournalSpecial Matrices
    Volume6
    Issue number1
    DOIs
    Publication statusPublished - 2018
    Publication typeA1 Journal article-refereed

    Keywords

    • Euclidean norm
    • Frobenius norm
    • generalized Fibonacci numbers
    • r-circulant matrix
    • spectral norm

    Publication forum classification

    • Publication forum level 1

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