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

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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