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.
|Number of pages||10|
|Journal||Journal of Computational and Applied Mathematics|
|State||Published - Oct 1 2018|
Bibliographical notePublisher Copyright:
© 2018 Elsevier B.V.
- Bézout identity
- Christoffel–Darboux formula
- Orthogonal polynomials
ASJC Scopus subject areas
- Computational Mathematics
- Applied Mathematics