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

被引：4

作者：

Merikoski, Jorma K. ^{[1
]}

Haukkanen, Pentti ^{[1
]}

Mattila, Mika ^{[2
]}

Tossavainen, Timo ^{[3
]}

机构：

[1] Univ Tampere, Fac Nat Sci, FI-33014 Tampere, Finland

[2] Tampere Univ Technol, Dept Math, POB 553, FI-33101 Tampere, Finland

[3] Lulea Univ Technol, Dept Arts Commun & Educ, SE-97187 Lulea, Sweden

来源：

SPECIAL MATRICES | 2018年 / 6卷 / 01期

关键词：

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

D O I：

10.1515/spma-2018-0003

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Consider the recursion g(0) = a, g(1) = b, g(n) = g(n-1) + g(n-2), n = 2, 3, . . . . We compute the Frobenius norm of the r-circulant matrix corresponding to g(0), . . . , 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.

引用

页码：23 / 36

页数：14

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