Optimal systems of nodes for Lagrange interpolation on bounded intervals. A survey

By G. Mastroianni, D. Occorsio. 2001

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A SPECTRAL METHOD FOR PANTOGRAPH-TYPE DELAY DIFFERENTIAL EQUATIONS AND ITS CONVERGENCE ANALYSIS * (2009, methodology): “From [11], we have the following result on the Lebesgue constant for Lagrange interpolation based on the zeros of the Legendre polynomials.”
Solving elliptic problems with non-Gaussian spatially-dependent random coefficients (2009, methodology): “For a onedimensional interpolation formula, the optimal order of the Lebesgue constant is logðmþ 1Þ with m being the polynomial order [24].”
Spectral methods for pantograph-type differential and integral equations with multiple delays (2009, methodology): “[13], we have the following result on the Lebesgue constant for Lagrange interpolation based on the zeros of the Legendre polynomials.”
Convergence Analysis of the Spectral Methods for Weakly Singular Volterra Integro-Differential Equations with Smooth Solutions (2012, background): “(see [19]) Let {F̂j(x)}j=0 be the N-th Lagrange interpolation polynomials associated with the Gauss points {θ̂k} k=0 of the Jacobi polynomials.”
Convergence analysis of Jacobi spectral collocation methods for Abel-Volterra integral equations of second kind (2012, unknown): “From [15, Theorem 1], we have the following weighted mean convergence result of Lagrange interpolation based at the zeros of Jacobi polynomials.”
Spectral-Collocation Methods for Fractional Pantograph Delay-Integrodifferential Equations (2013, unknown): “Lemma 3 (see [28]).”