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ASSR Matrices and Some Particular Cases

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Computational Mathematics, Numerical Analysis and Applications

Part of the book series: SEMA SIMAI Springer Series ((SEMA SIMAI,volume 13))

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Abstract

A real matrix is said Almost Strictly Sign Regular (ASSR) if all its nontrivial minors of the same order have the same strict sign. In this research, nonsingular ASSR matrices are characterized through the Neville elimination (NE). In addition, the algorithm is simplified for two important subclases: almost strictly totally negative (ASTN) matrices and Jacobi (tridiagonals) ASSR matrices.

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References

  1. Alonso, P., Peña, J.M., Serrano, M.L.: On the characterization of almost strictly sign regular matrices. J. Comput. Appl. Math. 275, 480–488 (2015)

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  2. Alonso, P., Peña, J.M., Serrano, M.L.: Characterizations of M-banded ASSR matrices. In: Trends in Differential Equations and Applications, pp. 33–49. Springer International Publishing, Cham (2016)

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  3. Gasca, M., Peña, J.M.: A test for strictly sign-regularity. Linear Algebra Appl. 198, 133–142 (1994)

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  4. Gasca, M., Peña, J.M.: A matricial description of Neville elimination with applications to total positivity. Linear Algebra Appl. 202, 33–54 (1994)

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Acknowledgements

This work has been partially supported by the Spanish Research Grant MTM2015-65433-P (MINECO/FEDER) and MTM2015-68805-REDT.

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Authors and Affiliations

  1. University of Oviedo, Oviedo, Spain

    P. Alonso & M. L. Serrano

  2. University of Zaragoza, Zaragoza, Spain

    J. M. Peña

Authors
  1. P. Alonso
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  2. J. M. Peña
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  3. M. L. Serrano
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Corresponding author

Correspondence to M. L. Serrano .

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Editors and Affiliations

  1. Matemáticas, Universidad de Oviedo , Gijón, Asturias, Spain

    Mariano Mateos

  2. Matemáticas, Universidad de Oviedo , Gijón, Asturias, Spain

    Pedro Alonso

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Alonso, P., Peña, J.M., Serrano, M.L. (2017). ASSR Matrices and Some Particular Cases. In: Mateos, M., Alonso, P. (eds) Computational Mathematics, Numerical Analysis and Applications. SEMA SIMAI Springer Series, vol 13. Springer, Cham. https://doi.org/10.1007/978-3-319-49631-3_12

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