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- W2074535821 abstract "This paper discusses the problem of choosing the Lagrange interpolation points T = ( t 0 , t 1 ,…, t n ) in the interval −1 ⩽ t ⩽ 1 to minimize the norm of the error, considered as an operator from the Hardy space H 2 ( R ) of analytic functions to the space C [−1, 1]. It is shown that such optimal choices converge for fixed n , as R → ∞, to the zeros of a Chebyshev polynomial. Asymptotic estimates are given for the norm of the error for these optimal interpolations, as n → ∞ for fixed R . These results are then related to the problem of choosing optimal interpolation points with respect to the Eberlein integral. This integral is based on a probability measure over certain classes of analytic functions, and is used to provide an average interpolation error over these classes. The Chebyshev points are seen to be limits of optimal choices in this case also." @default.
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- W2074535821 date "1977-12-01" @default.
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- W2074535821 title "On optimal polynomial interpolation of analytic functions" @default.
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- W2074535821 doi "https://doi.org/10.1016/0021-9045(77)90008-9" @default.
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