Abstract
In this paper, we find uniform asymptotic formulas for all the eigenvalues of certain pentadiagonal symmetric Toeplitz matrices of large dimension. The entries of the matrices are real and we consider the case where the real-valued generating function has a minimum and a maximum such that its fourth derivative at the minimum and its second derivative at the maximum are nonzero. This is not the simple-loop case considered in [1] and [2]. We apply the main result of [7] and obtain nonlinear equations for the eigenvalues. It should be noted that our equations have a more complicated structure than the equations in [1] and [2]. Therefore, we required a more delicate method for its asymptotic analysis.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
