Sturm theorem for the generalized Frank matrix

Year 2021, Volume: 50 Issue: 4, 1002 - 1011, 06.08.2021

Efruz Özlem Mersin Mustafa Bahşi

https://doi.org/10.15672/hujms.773281

Cited By: 3

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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