Alternation points and bivariate Lagrange interpolation

Lawrence A. Harris

Research output: Contribution to journalArticlepeer-review

4 Scopus citations


Given m+1 strictly decreasing numbers h0,h1,…,hm, we give an algorithm to construct a corresponding finite sequence of orthogonal polynomials p0,p1,…,pm such that p0=1, pj has degree j and pm−j(hn)=(−1)npj(hn) for all j,n=0,1,…,m. Using these polynomials, we construct bivariate Lagrange polynomials and cubature formulas for nodes that are points in R2 where the coordinates are taken from given finite decreasing sequences of the same length and where the indices have the same (or opposite) parity.

Original languageEnglish
Pages (from-to)43-52
Number of pages10
JournalJournal of Computational and Applied Mathematics
StatePublished - Oct 1 2018

Bibliographical note

Publisher Copyright:
© 2018 Elsevier B.V.


  • Bézout identity
  • Christoffel–Darboux formula
  • Cubature
  • Orthogonal polynomials

ASJC Scopus subject areas

  • Computational Mathematics
  • Applied Mathematics


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