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

Jorma K. Merikoski; Pentti Haukkanen; Mika Mattila; Timo Tossavainen

doi:10.1515/spma-2018-0003

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

Jorma K. Merikoski, Pentti Haukkanen, Mika Mattila, Timo Tossavainen

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Abstract

Consider the recursion g₀ = a, g₁ = b, g_n = g_n-1 + g_n-2, n = 2, 3, . . . . We compute the Frobenius norm of the r-circulant matrix corresponding to g₀, . . . , g_n-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 language	English
Pages (from-to)	23-36
Number of pages	14
Journal	Special Matrices
Volume	6
Issue number	1
DOIs	https://doi.org/10.1515/spma-2018-0003
Publication status	Published - 2018
Publication type	A1 Journal article-refereed

Keywords

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

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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.",

keywords = "Euclidean norm, Frobenius norm, generalized Fibonacci numbers, r-circulant matrix, spectral norm, Euclidean norm, Frobenius norm, generalized Fibonacci numbers, r-circulant matrix, spectral norm",

author = "Merikoski, {Jorma K.} and Pentti Haukkanen and Mika Mattila and Timo Tossavainen",

year = "2018",

doi = "10.1515/spma-2018-0003",

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T1 - On the spectral and Frobenius norm of a generalized Fibonacci r-circulant matrix

AU - Merikoski, Jorma K.

AU - Haukkanen, Pentti

AU - Mattila, Mika

AU - Tossavainen, Timo

PY - 2018

Y1 - 2018

N2 - 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.

AB - 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.

KW - Euclidean norm

KW - Frobenius norm

KW - generalized Fibonacci numbers

KW - r-circulant matrix

KW - spectral norm

KW - Euclidean norm

KW - Frobenius norm

KW - generalized Fibonacci numbers

KW - r-circulant matrix

KW - spectral norm

U2 - 10.1515/spma-2018-0003

DO - 10.1515/spma-2018-0003

M3 - Article

AN - SCOPUS:85042290997

SN - 2300-7451

VL - 6

SP - 23

EP - 36

JO - Special Matrices

JF - Special Matrices

IS - 1

ER -

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

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Keywords

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