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

Authors : Efruz Özlem Mersin, Mustafa Bahşi

Pages : 420-436

Doi:10.31801/cfsuasmas.1299736

View : 30 | Download : 45

Publication Date : 2024-06-21

Article Type : Research Paper

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