69
Views
0
CrossRef citations to date
0
Altmetric
Original Articles

Algorithmic characterization of pentadiagonal ASSR matrices

ORCID Icon, &
Pages 431-443 | Received 31 May 2019, Accepted 27 Jun 2019, Published online: 15 Jul 2019

References

  • P. Alonso, R. Cortina, I. Díaz, and J. Ranilla, Scalability of Neville elimination using checkerboard partitioning, Int. J. Comput. Math. 85 (2008), pp. 309–317. doi: 10.1080/00207160601167078
  • P. Alonso, J. Delgado, R. Gallego, and J.M. Peña, Iterative refinement for neville elimination, Int. J. Comput. Math. 34 (2009), pp. 341–353. doi: 10.1080/00207160802044134
  • P. Alonso, J.M. Peña, and M.L. Serrano, On the characterization of almost strictly sign regular matrices, J. Comput. Appl. Math. 275 (2015), pp. 480–488. doi: 10.1016/j.cam.2014.01.032
  • P. Alonso, J.M. Peña, and M.L. Serrano, Almost strictly sign regular matrices and Neville elimination with two-determinant pivoting, Appl. Math. Comput. 289 (2016), pp. 426–434.
  • P. Alonso, J.M. Peña, and M.L. Serrano, Characterizations of M-banded ASSR matrices, in Trends in Differential Equations and Applications, F. Ortegón, M.V. Redondo and J.R. Rodríguez, eds., Springer International Publishing, Cham, 2016, pp. 33–49.
  • P. Alonso, J.M. Peña, and M.L. Serrano, Comparing pivoting strategies for almost strictly sign regular matrices, J. Comput. Appl. Math. 354 (2019), pp. 96–102. doi: 10.1016/j.cam.2018.02.015
  • T. Ando, Total positive matrices, Linear Algebra Appl. 90 (1987), pp. 165–219. doi: 10.1016/0024-3795(87)90313-2
  • A. Barreras and J.M. Peña, On tridiagonal sign regular matrices and generalizations, in Advances in Differential Equations and Applications, F. Casas and V. Martínez, eds., SEMA, SIMAi Springer Series, Cham, 2014, pp. 239–247.
  • L.D. Brown, I.M. Johnstone, and K.B. MacGibbon, Variation diminishing transformations: A direct approach to total positivity and its statistical applications, J. Amer. Statist. Assoc 76 (1981), pp. 824–832. doi: 10.1080/01621459.1981.10477730
  • V. Cortés and J.M. Peña, Sign regular matrices and Neville elimination, Linear Algebra Appl. 421 (2007), pp. 53–62. doi: 10.1016/j.laa.2006.03.040
  • S.M. Fallat and C.R. Johnson, Totally Nonnegative Matrices, Princeton University Press, Princeton, NJ, 2011.
  • F.P. Gantmacher and M.G. Krein, Oscillation Matrices and Kernels and Small Vibrations of Mechanical Systems, AMS Chelsea, Providence, RI, 2002.
  • M. Gasca, C.A. Micchelli, and J.M. Peña, Almost strictly totally positive matrices, Numer. Algorithms 2 (1992), pp. 225–236. doi: 10.1007/BF02145387
  • M. Gasca and J.M. Peña, Total positiviy and Neville elimination, Linear Algebra Appl. 165 (1992), pp. 25–44. doi: 10.1016/0024-3795(92)90226-Z
  • M. Gasca and J.M. Peña, A matricial description of neville elimination with application to total positivity, Linear Algebra Appl. 202 (1994), pp. 33–54. doi: 10.1016/0024-3795(94)90183-X
  • M. Gasca and J.M. Peña, On the characterization of almost strictly total positive matrices, Adv. Comp. Math. 3 (1995), pp. 239–250. doi: 10.1007/BF02432001
  • R. Huang, Nonsingular almost strictly sign regular matrices, Linear Algebra Appl. 436 (2012), pp. 4179–4192. doi: 10.1016/j.laa.2012.01.012
  • S. Karlin, Total Positivity, Stanford University Press, London, 1968.
  • A. Pinkus, Total positive matrices, Cambridge University Press, Cambridge, 2009.
  • I.J. Schoenberg, Uber Variationsverminderende lineare Transformationen, Math. Z. 32 (1930), pp. 321–328. doi: 10.1007/BF01194637

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.