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Special Matrices

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CiteScore 2017: 0.29

SCImago Journal Rank (SJR) 2017: 0.295
Source Normalized Impact per Paper (SNIP) 2017: 0.481

Mathematical Citation Quotient (MCQ) 2017: 0.17

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2300-7451
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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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  • Department of Arts, Communication and Education, Lulea University of Technology, SE-97187 Lulea, Sweden
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Published Online: 2018-01-24 | DOI: https://doi.org/10.1515/spma-2018-0003

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

References

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About the article

Received: 2017-10-09

Accepted: 2017-12-26

Published Online: 2018-01-24


Citation Information: Special Matrices, Volume 6, Issue 1, Pages 23–36, ISSN (Online) 2300-7451, DOI: https://doi.org/10.1515/spma-2018-0003.

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© 2018, published by De Gruyter. This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License. BY-NC-ND 4.0

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