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

Year 2024, Volume: 73 Issue: 2, 420 - 436, 21.06.2024

Efruz Özlem Mersin , Mustafa Bahşi

https://doi.org/10.31801/cfsuasmas.1299736

Cited By: 2

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.

Keywords

Fibonacci sequence, Lucas sequence, Frank matrix, eigenvalue, bounds, norm

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