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Journals / Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics / 2026 / Volume: 73 Issue: 2

Bounds for the maximum eigenvalues of the Fibonacci-Frank and Lucas-Frank matrices

Efruz Özlem Mersin(AKSARAY UNIVERSITY)0000-0001-6260-9063
Mustafa Bahşi(AKSARAY UNIVERSITY)0000-0002-6356-6592
Pages
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Publication Date
2024-06-21
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AI Summary & Key Takeaways

AI Insight
⚡ TL;DR(Too Long; Didn't Read)

Then, we obtain the Euclidean norms and the upper bounds for the spectral norms of these matrices.

📌 3 Key Takeaways

🎯
Objective & Hypothesis:Frank matrix is one of the popular test matrices for eigenvalue routines because it has well-conditioned and poorly conditioned eigenvalues.
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Key Findings & Data:In this paper, we investigate the bounds for the maximum eigenvalues of the special cases of the generalized Frank matrices which are called Fibonacci-Frank and Lucas-Frank matrices.
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Conclusion & Impact:Then, we obtain the Euclidean norms and the upper bounds for the spectral norms of these matrices.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:Fibonacci sequence · Lucas sequence · Frank matrix

Abstract

Frank matrix is one of the popular test matrices for eigenvalue routines because it has well-conditioned and poorly conditioned eigenvalues. In this paper, we investigate the bounds for the maximum eigenvalues of the special cases of the generalized Frank matrices which are called Fibonacci-Frank and Lucas-Frank matrices. Then, we obtain the Euclidean norms and the upper bounds for the spectral norms of these matrices.

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Cite This Article

Mersin, E. Ö., Bahşi, M. (2024). Bounds for the maximum eigenvalues of the Fibonacci-Frank and Lucas-Frank matrices. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, Volume: 73 Issue: 2. https://doi.org/10.31801/cfsuasmas.1299736

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