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Approximating the eigenvalues and eigenvectors of birth and death matrices

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Abstract

The objective of this note is to approximate a birth and death matrix B by a close Toeplitz-type one for which explicit formulas for the eigenpairs are known. Numerical evidence of the approximation behavior of the eigenvalues and eigenvectors of B by those of such Toeplitz-type matrices is provided.

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Acknowledgements

The authors thank the referees for the valuable suggestions.

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Authors and Affiliations

  1. CMUC and Departamento de Matemática, Universidade de Coimbra, 3001-454, Coimbra, Portugal

    Natália Bebiano

  2. CEAFEL and Faculdade de Economia do Porto, Universidade do Porto, 4200-464, Porto, Portugal

    Susana Furtado

Authors
  1. Natália Bebiano
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  2. Susana Furtado
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Corresponding author

Correspondence to Susana Furtado.

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Communicated by Jinyun Yuan.

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This work was partially supported by project UID/MAT/00324/2019. This work was partially supported by FCT- Fundação para a Ciência e Tecnologia, under project UID/MAT/04721/2020.

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Bebiano, N., Furtado, S. Approximating the eigenvalues and eigenvectors of birth and death matrices. Comp. Appl. Math. 39, 279 (2020). https://doi.org/10.1007/s40314-020-01327-z

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  • DOI: https://doi.org/10.1007/s40314-020-01327-z

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