On Mean Convergence of Lagrange-Kronrod Interpolation
It is known that Lagrange interpolation to any continuous function on [-1, 1] at the zeros of an orthogonal polynomial converges in the mean. In this paper we study mean convergence of Lagrange-Kronrod interpolation where the nodes are the n zeros of an orthogonal polynomial of degree n and the n + 1 zeros of the associated Stieltjes polynomial of degree n + 1. A sufficient condition for mean convergence, due to P. Erdös and P. Turán, is shown to hold for the first-, the third- and fourth-kind Chebyshev weight functions.
KeywordsWeight Function Orthogonal Polynomial Quadrature Formula Lagrange Interpolation Lagrange Interpolation Polynomial
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