45 citations · 194 across the 100 of their papers we have counts for
18 papers · 1 filter
Orthogonal polynomials on a class of planar algebraic curves
Marco Fasondini, Sheehan Olver, Yuan Xu
We construct bivariate orthogonal polynomials (OPs) on algebraic curves of the form in where and is a polynomial of arbitrary degree ,…
Orthogonal polynomials on planar cubic curves
Marco Fasondini, Sheehan Olver, Yuan Xu
Orthogonal polynomials in two variables on cubic curves are considered, including the case of elliptic curves. For an integral with respect to an appropriate weight function define…
Orthogonal structure on a quadratic curve
Sheehan Olver, Yuan Xu
Orthogonal polynomials on quadratic curves in the plane are studied. These include orthogonal polynomials on ellipses, parabolas, hyperbolas, and two lines. For an integral with re…
Optimal Points for Cubature Rules and Polynomial Interpolation on a Square
Yuan Xu
The nodes of certain minimal cubature rule are real common zeros of a set of orthogonal polynomials of degree . They often consist of a well distributed set of points and interp…
Minimal Cubature rules and polynomial interpolation in two variables II
Yuan Xu
As a complement to \cite{X12}, minimal cubature rules of degree for the weight functions $$ \mathcal{W}_{α,β,\pm \frac12}(x,y) = |x+y|^{2α+1} |x-y|^{2β+1} ((1-x^2)(1-y^2))^{…
Minimal cubature rules on an unbounded domain
Yuan Xu
A family of minimal cubature rules is established on an unbounded domain, which is the first such family known on unbounded domains. The nodes of such cubature rules are common zer…