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Dergiler / Hacettepe Journal of Mathematics and Statistics / 2021 / Cilt: 50 - Sayı: 4

Sturm theorem for the generalized Frank matrix

Efruz Özlem Mersin
Mustafa Bahşi
Sayfa
1002–1011
Yayın Tarihi
2022-10-18
DOI
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Moreover, we illustrate our results with an example.

📌 3 Maddede Bu Makale

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Amaç & Hipotez:One of the popular test matrices for eigenvalue routines is the Frank matrix due to its well-conditioned and poorly conditioned eigenvalues.
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Temel Bulgular & Veri:All the eigenvalues of the Frank matrix are real, positive and different.
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Sonuç & Katkı:Moreover, we illustrate our results with an example.
🔬Tür:Araştırma Makalesi
📍Kapsam:Genişletilmiş Akademik Örneklem
⚙️Değişkenler:Sturm Sequence · Characteristic Polynomial · Eigenvalue

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.

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Bu Makaleye Atıf Yap

Mersin, E. Ö., Bahşi, M. (2022). Sturm theorem for the generalized Frank matrix. Hacettepe Journal of Mathematics and Statistics, Cilt: 50 - Sayı: 4, 1002–1011. https://ajindex.com/articles/529475

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