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Optimal Points for Cubature Rules and Polynomial Interpolation on a Square

Chapter

Abstract

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.

Notes

Acknowledgements

The author thanks two anonymous referees for their careful reading and corrections. The work was supported in part by NSF Grant DMS-1510296.

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© Springer International Publishing AG, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Department of MathematicsUniversity of OregonEugeneUSA

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