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Accurate Algorithms for Bessel Matrices

  • Jorge DelgadoEmail author
  • Héctor Orera
  • J. M. Peña
Article
  • 16 Downloads

Abstract

In this paper, we prove that any collocation matrix of Bessel polynomials at positive points is strictly totally positive, that is, all its minors are positive. Moreover, an accurate method to construct the bidiagonal factorization of these matrices is obtained and used to compute with high relative accuracy the eigenvalues, singular values and inverses. Similar results for the collocation matrices for the reverse Bessel polynomials are also obtained. Numerical examples illustrating the theoretical results are included.

Keywords

Bessel matrices Totally positive matrices High relative accuracy Bessel polynomials Reverse Bessel polynomials 

Mathematics Subject Classification

65F05 65F15 65G50 33C10 33C45 15A23 

Notes

Acknowledgements

This work was partially supported through the Spanish research grant PGC2018-096321-B-I00 (MCIU/AEI), by Gobierno de Aragón (E41_17R) and by Feder 2014-2020 “Construyendo Europa desde Aragon”.

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Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Departamento de Matemática Aplicada, Escuela Universitaria Politécnica de TeruelUniversidad de ZaragozaTeruelSpain
  2. 2.Departamento de Matemática Aplicada, Facultad de CienciasUniversidad de ZaragozaZaragozaSpain

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