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Arabian Journal of Mathematics

, Volume 8, Issue 1, pp 55–62 | Cite as

On the characterization of the degree of interpolation polynomials in terms of certain combinatorical matrices

  • Frank KlinkerEmail author
  • Christoph Reineke
Open Access
Article
First Online:

Abstract

In this note, we show that the degree of the interpolation polynomial for equidistant base points is characterized by the regularity of matrices of combinatorical type.

Mathematics Subject Classification

65D05 15B36 15A15 
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Notes

References

  1. 1.
    De Marchi, S.: Polynomials arising in factoring generalized Vandermonde determinants: an algorithm for computing their coefficients. Math. Comput. Model. 34(3/4), 271–281 (2001)MathSciNetCrossRefGoogle Scholar
  2. 2.
    de Camargo, A.P.: Schur functions through Lagrange polynomials. J. Pure Appl. Algebra 220(8), 2948–2954 (2016)MathSciNetCrossRefGoogle Scholar
  3. 3.
    Davis, P.J.: Interpolation and Approximation. Dover Publication Inc, New York (1975)zbMATHGoogle Scholar
  4. 4.
    Deuflhard, P.; Hohmann, A.: Numerical Analysis in Modern Scientific Computing. Springer, New York (2003)CrossRefGoogle Scholar
  5. 5.
    Heineman, E.R.: Generalized Vandermonde determinants. Trans. Am. Math. Soc. 31(3), 464–476 (1929)MathSciNetCrossRefGoogle Scholar
  6. 6.
    King, R.C.: Generalised Vandermonde determinants and Schur functions. Proc. Am. Math. Soc. 48(1), 53–56 (1975)MathSciNetCrossRefGoogle Scholar
  7. 7.
    Klinker, F., Reineke, C.: On the regularity of matrices with uniform polynomial entries. Sao Paulo J. Math. Sci. (2018), online 2017Google Scholar
  8. 8.
    Krattenthaler, C.: Advanced determinant calculus. Sem. Lothar. Combin. 42 Art. B42q, 67 (1999)Google Scholar
  9. 9.
    Krattenthaler, C.: Advanced determinant calculus: a complement. Linear Algebra Appl. 411, 68–166 (2005)MathSciNetCrossRefGoogle Scholar
  10. 10.
    Littlewood, D.E.: The Theory of Group Characters and Matrix Representations of Groups. Oxford University Press, New York (1940)zbMATHGoogle Scholar
  11. 11.
    Riordan, J.: Combinatorical Identities. Reprint of the 1968 Original. Robert E. Krieger Publishing Co., Huntington (1979)Google Scholar

Copyright information

© The Author(s) 2018

Open AccessThis article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.

Authors and Affiliations

  1. 1.Faculty of MathematicsTU Dortmund UniversityDortmundGermany

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