Optimal Points for Cubature Rules and Polynomial Interpolation on a Square
arXiv:1709.006511.22 citations
Originality Synthesis-oriented
AI Analysis
Provides theoretical foundations for constructing accurate cubature and interpolation on squares, relevant for numerical analysis.
The paper reviews minimal cubature rules on a square, where nodes are common zeros of orthogonal polynomials, and shows that interpolation based on these nodes achieves good convergence.
The nodes of certain minimal cubature rule are real common zeros of a set of orthogonal polynomials of degree $n$. They often consist of a well distributed set of points and interpolation polynomials based on them have desired convergence behavior. We report what is known and the theory behind by explaining the situation when the domain of integrals is a square.