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Siberian Mathematical Journal

, Volume 54, Issue 3, pp 425–430 | Cite as

Sufficient conditions for the nonnegativity of solutions to a system of equations with a nonstrictly jacobian matrix

  • V. V. BogdanovEmail author
Article
  • 43 Downloads

Abstract

For the tridiagonal system of linear algebraic equations whose matrix is nonstrictly Jacobi diagonally dominant in columns we establish sufficient conditions for all components of the solution to be nonnegative.

Keywords

system of linear equations matrix of monotone kind tridiagonal matrix nonnegative solution 

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References

  1. 1.
    Collatz L., Functional Analysis and Computational Mathematics, Academic Press, New York and London (1966).Google Scholar
  2. 2.
    Miroshnichenko V. L., “Convex and monotone spline interpolation,” in: Constructive Theory of Functions’84, Sofia, 1984, pp. 610–620.Google Scholar
  3. 3.
    Miroshnichenko V. L., “Sufficient conditions for monotonicity and convexity for interpolation of cubic splines of the class C 2,” in: Approximation by Splines (Vychisl. Sistemy, No. 137) [in Russian], Inst. Mat., Novosibirsk, 1990, pp. 31–57.Google Scholar
  4. 4.
    Miroshnichenko V. L., “Sufficient conditions for monotonicity and convexity for interpolation parabolic splines,” in: Splines and Their Applications (Vychisl. Sistemy, No. 142) [in Russian], Inst. Mat., Novosibirsk, 1991, pp. 3–14.Google Scholar
  5. 5.
    Miroshnichenko V. L., “Isogeometric properties and approximation error of weighted cubic splines,” in: Splines and Their Applications (Vychisl. Sistemy, No. 154) [in Russian], Inst. Mat., Novosibirsk, 1995, pp. 127–154.Google Scholar
  6. 6.
    Miroshnichenko V. L., “Optimization of the form of the rational spline,” in: Spline-Functions and Their Applications (Vychisl. Sistemy, No. 159) [in Russian], Inst. Mat., Novosibirsk, 1997, pp. 87–109.Google Scholar
  7. 7.
    Zav’yalov Yu. S., “Monotone interpolation by generalized cubic splines of the class C 2,” in: Interpolation and Approximation by Splines (Vychisl. Sistemy, No. 147) [in Russian], Inst. Mat., Novosibirsk, 1992, pp. 44–67.Google Scholar
  8. 8.
    Zav’yalov Yu. S., “Convex interpolation by generalized cubic splines of the class C 2,” in: Splines and Their Applications (Vychisl. Sistemy, No. 154) [in Russian], Inst. Mat., Novosibirsk, 1995, pp. 15–64.Google Scholar
  9. 9.
    Volkov Yu. S., “On monotone interpolation by cubic splines,” Vychisl. Tekhnol., 6, No. 6, 14–24 (2001).MathSciNetzbMATHGoogle Scholar
  10. 10.
    Volkov Yu. S., “A new method for constructing cubic interpolating splines,” Comput. Math. Math. Physics, 44, No. 2, 215–224 (2004).Google Scholar
  11. 11.
    Bogdanov V. V. and Volkov Yu. S., “Selection of parameters of generalized cubic splines with convexity preserving interpolation,” Sibirsk. Zh. Vychisl. Mat., 9, No. 1, 5–22 (2006).zbMATHGoogle Scholar
  12. 12.
    Bogdanov V. V., Volkov Yu. S., Miroshnichenko V. L., and Shevaldin V. T., “Shape-preserving interpolation by cubic splines,” Math. Notes, 88, No. 6, 798–805 (2010).MathSciNetzbMATHGoogle Scholar
  13. 13.
    Volkov Yu. S., “Nonnegative solutions to systems with symmetric circulant matrix,” Math. Notes, 70, No. 2, 154–162 (2001).MathSciNetzbMATHCrossRefGoogle Scholar
  14. 14.
    Zav’yalov Yu. S., “On a nonnegative solution of a system of equations with a nonstrictly Jacobian matrix,” Siberian Math. J., 37, No. 6, 1143–1147 (1996).MathSciNetzbMATHCrossRefGoogle Scholar
  15. 15.
    Bogdanov V. V., “Sufficient conditions for the comonotone interpolation of cubic C 2,” Siberian Adv. in Math., 22, No. 3, 153–160 (2012).MathSciNetCrossRefGoogle Scholar

Copyright information

© Pleiades Publishing, Ltd. 2013

Authors and Affiliations

  1. 1.Sobolev Institute of MathematicsNovosibirskRussia

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