Lagrange interpolation on Chebyshev points of two variables
Journal of Approximation Theory
On minimal cubature formulae for product weight functions
Journal of Computational and Applied Mathematics
On the Lebesgue constant for the Xu interpolation formula
Journal of Approximation Theory
On multivariate projection operators
Journal of Approximation Theory
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Minimal cubature rules of degree 4n-1 for the weight functions W"@a","@b","+/-"1"2(x,y)=|x+y|^2^@a^+^1|x-y|^2^@b^+^1((1-x^2)(1-y^2))^+/-^1^2 on [-1,1]^2 are constructed explicitly and are shown to be closely related to the Gaussian cubature rules in a domain bounded by two lines and a parabola. Lagrange interpolation polynomials on the nodes of these cubature rules are constructed and their Lebesgue constants are determined.