Accurate computations with generalized Frank matrices and total positivity

Héctor Orera; J. M. Peña; Héctor Orera; J. M. Peña

doi:10.3934/math.20261059

AIMS Mathematics

2026, Volume 11, Issue 8: 26397-26408. doi: 10.3934/math.20261059

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Research article

Accurate computations with generalized Frank matrices and total positivity

Héctor Orera ^,,
J. M. Peña

Departamento de Matemática Aplicada/IUMA, Facultad de Ciencias, Universidad de Zaragoza, Calle de Pedro Cerbuna, 12, Zaragoza, 50009, Spain

Received: 22 April 2026 Revised: 13 August 2026 Accepted: 18 August 2026 Published: 24 August 2026
MSC : 65G50, 15A23, 65F05, 65F15

Total positivity of a class of generalized Frank matrices is proved. A bidiagonal decomposition of these matrices is obtained with high relative accuracy (HRA). It can be applied to compute their singular values, eigenvalues, inverses, or solutions of linear systems with HRA. Numerical tests confirming the theoretical results are included. They show that the proposed methods outperform standard numerical algorithms.
- total positivity,
- bidiagonal decompositions,
- frank matrix,
- accurate computations
Citation: Héctor Orera, J. M. Peña. Accurate computations with generalized Frank matrices and total positivity[J]. AIMS Mathematics, 2026, 11(8): 26397-26408. doi: 10.3934/math.20261059

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Abstract

Total positivity of a class of generalized Frank matrices is proved. A bidiagonal decomposition of these matrices is obtained with high relative accuracy (HRA). It can be applied to compute their singular values, eigenvalues, inverses, or solutions of linear systems with HRA. Numerical tests confirming the theoretical results are included. They show that the proposed methods outperform standard numerical algorithms.

References

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