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Research Article

Characterizations and accurate computations for tridiagonal Toeplitz matrices

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Pages 4508-4527 | Received 23 Jan 2020, Accepted 27 Jan 2021, Published online: 13 Feb 2021

References

  • Demmel J, Dumitriu I, Holtz O, et al. Accurate and efficient expression evaluation and linear algebra. Acta Numer. 2008;17:87–145.
  • Elouafi M. Explicit inversion of band Toeplitz matrices by discrete Fourier transform. Linear Multilinear Algebra. 2018;66:1767–1782.
  • Luati A, Proietti T. On the spectral properties of matrices associated with trend filters. Econ Theory. 2010;26:1247–1261.
  • Noschese S, Pasquini L, Reichel L. Tridiagonal Toeplitz matrices: properties and novel applications. Numer Linear Algebra Appl. 2013;20:302–326.
  • Noschese S, Reichel L. Eigenvector sensitivity under general and structured perturbations of tridiagonal Toeplitz-type matrices. Numer. Linear Algebra Appl. 2019;26:e2232.
  • Reichel L, Ye Q. Simple square smoothing regularization operators. Electron Trans Numer Anal. 2009;33:63–83.
  • Smith GD. Numerical solution of partial differential equations: finite difference methods. 3rd ed. New York (NY): Oxford University Press; 1985.
  • Došlić T, Martinjak I, Škrekovski R. Total positivity of Toeplitz matrices of recursive hypersequences. Ars Math Contemp. 2019;17:126–139.
  • Jia J. A breakdown-free algorithm for computing the determinants of periodic tridiagonal matrices. Numer Algorithms. 2020;83:149–163.
  • Ando T. Totally positive matrices. Linear Algebra Appl. 1987;90:165–219.
  • Gasca M, Micchelli CA. Total positivity and its applications: mathematics and its applications. Dordrecht (Amsterdam): Kluwer Academic Publishers Group; 1996.
  • Pinkus A. Totally positive matrices. Cambridge (UK): Cambridge University Press; 2010.
  • Berman A, Plemmons RJ. Nonnegative matrices in the mathematical sciences. Philadelphia (PA): Society for Industrial and Applied Mathematics (SIAM); 1994. (Classics in Applied Mathematics; vol. 9).
  • Demmel J, Koev P. The accurate and efficient solution of a totally positive generalized Vandermonde linear system. SIAM J Matrix Anal Appl. 2005;27:142–152.
  • Koev P. Accurate computations with totally nonnegative matrices. SIAM J Matrix Anal Appl. 2007;29:731–751.
  • Delgado J, Orera H, Peña JM. Accurate computations with Laguerre matrices. Numer Linear Algebra Appl. 2019;26:e2217.
  • Delgado J, Orera H, Peña JM. Accurate algorithms for Bessel matrices. J Sci Comput. 2019;80:1264–1278.
  • Delgado J, Peña JM. Accurate computations with collocation matrices of q-Bernstein polynomials. SIAM J Matrix Anal Appl. 2015;36:880–893.
  • Delgado J, Peña JM, Accurate computations with Lupaş matrices. Appl Math Comput. 2017;303:171–177.
  • Marco A, Martínez J-J, A total positivity property of the Marchenko-Pastur law. Electron J Linear Algebra. 2015;30:106–117.
  • Marco A, Martínez J-J. Bidiagonal decomposition of rectangular totally positive Said-Ball-Vandermonde matrices: error analysis, perturbation theory and applications. Linear Algebra Appl. 2016;495:90–107.
  • Marco A, Martínez J-J, Viaña R. Accurate bidiagonal decomposition of totally positive h-Bernstein-Vandermonde matrices and applications. Linear Algebra Appl. 2019;579:320–335.
  • Koev P. Accurate eigenvalues and SVDs of totally nonnegative matrices. SIAM J Matrix Anal Appl. 2005;27:1–23.
  • Koev P. [cited 2020 Jan 16]. Available From: http://www.math.sjsu.edu/koev/software/TNTool.html
  • Horn RA, Johnson CR. Topics in matrix analysis. Cambridge (UK): Cambridge University Press; 1991.
  • Barreras A, Peña JM. On tridiagonal sign regular matrices and generalizations. In: Casas F, Martínez V, editors. Advances in differential equations and applications. Cham (Switzerland): Springer International Publishing Switzerland; 2014. p. 239–248.
  • Alonso P, Cortina R, Ranilla J, et al. An efficient and scalable block parallel algorithm of Neville elimination as a tool for the CMB maps problem. J Math Chem. 2012;50:345–358.
  • Gasca M, Peña JM. Total positivity and Neville elimination. Linear Algebra Appl. 1992;165:25–44.
  • Gasca M, Peña JM. On factorizations of totally positive matrices. In: Gasca M, Micchelli CA, editors. Total positivity and its applications. Dordrecht (Amsterdam): Kluwer Academic Publishers Group; 1996. p. 109–130.
  • Barreras A, Peña JM. Accurate computations of matrices with bidiagonal decomposition using methods for totally positive matrices. Numer Linear Algebra Appl. 2013;20:413–424.
  • Katkova O, Vishnyakova A. On sufficient conditions for the total positivity and for the multiple positivity of matrices. Linear Algebra Appl. 2006;416:1083–1097.
  • Kavčić A, Moura J. Matrices with banded inverses: inversion algorithms and factorization of Gauss–Markov processes. IEEE Trans Inf Theory. 2000;46:1495–1509.
  • Peña JM. M-matrices whose inverses are totally positive. Linear Algebra Appl. 1995;221:189–193.
  • da Fonseca CM, Petronilho J. Explicit inverses of some tridiagonal matrices. Linear Algebra Appl. 2001;325:7–21.

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