Sturm theorem for the generalized Frank matrix

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Hacettepe Journal of Mathematics and Statistics
Volume:50 Issue:4
Sturm theorem for the generalized Frank matrix

Sturm theorem for the generalized Frank matrix

Authors : Efruz Özlem MERSİN, Mustafa BAHŞİ

Pages : 1002-1011

Doi:10.15672/hujms.773281

View : 22 | Download : 16

Publication Date : 2021-08-06

Article Type : Research Paper

Abstract :One of the popular test matrices for eigenvalue routines is the Frank matrix due to its well-conditioned and poorly conditioned eigenvalues. All the eigenvalues of the Frank matrix are real, positive and different. Sturm Theorem is a very useful tool for computing the eigenvalues of tridiagonal symmetric matrices. In this paper, we apply Sturm Theorem to the generalized Frank matrix which is a special form of the Hessenberg matrix and examine its eigenvalues by using Sturm property. Moreover, we illustrate our results with an example.
Keywords : Sturm Sequence, Characteristic Polynomial, Eigenvalue, Frank Matrix

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