Birkhoff Polynomial Basis

  • Amir Amiraslani
  • Heike Faßbender
  • Nikta Shayanfar
Conference paper
Part of the Springer Proceedings in Mathematics & Statistics book series (PROMS, volume 192)


The Birkhoff interpolation problem is an extension of the well-known Lagrange and Hermite interpolation problems. We propose a new set of basis polynomials for representing the Birkhoff interpolation polynomial . The proposed basis extends the definition of the Newton basis for non-distinct interpolation nodes. This approach allows to determine the Birkhoff interpolation polynomial via a special linear system of equations. When applied to the special cases of Taylor, Lagrange and Hermite interpolations, this approach reduces to the well-known solutions of these problems expressed in the Newton basis . A number of examples are studied.


Polynomial bases Polynomial interpolation Differentiation matrix Birkhoff matrix 



Alexander von Humboldt Foundation has funded the work of third author.


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Copyright information

© Springer International Publishing AG 2017

Authors and Affiliations

  • Amir Amiraslani
    • 1
  • Heike Faßbender
    • 2
  • Nikta Shayanfar
    • 2
  1. 1.STEM DepartmentUniversity of Hawaii-Maui CollegeKahuluiUSA
  2. 2.Institut Computational MathematicsAG Numerik, Technische Universität BraunschweigBraunschweigGermany

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