Mean convergence of derivatives of Lagrange interpolation
نویسندگان
چکیده
منابع مشابه
On Mean Convergence of Lagrange Interpolation for General Arrays
For n 1, let fxjngnj=1 be n distinct points in a compact set K R and let Ln[ ] denote the corresponding Lagrange Interpolation operator. Let v be a suitably restricted function on K. What conditions on the array fxjng1 j n; n 1 ensure the existence of p > 0 such that lim n!1 k (f Ln[f ]) v kLp(K)= 0 for every continuous f :: K ! R ? We show that it is necessary and su cient that there exists r ...
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For n 1, let fxjngnj=1 be n distinct points and let Ln[ ] denote the corresponding Lagrange Interpolation operator. Let W : R ! [0;1). What conditions on the array fxjng1 j n; n 1 ensure the existence of p > 0 such that lim n!1 k (f Ln[f ])W b kLp(R)= 0 for every continuous f : R ! Rwith suitably restricted growth, and some weighting factor ? We obtain a necessary and su¢ cient condition for ...
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The authors give a procedure to construct extended interpolation formulae and prove some uniform convergence theorems.
متن کاملOn quadrature convergence of extended Lagrange interpolation
Quadrature convergence of the extended Lagrange interpolant L2n+1f for any continuous function f is studied, where the interpolation nodes are the n zeros τi of an orthogonal polynomial of degree n and the n+ 1 zeros τ̂j of the corresponding “induced” orthogonal polynomial of degree n + 1. It is found that, unlike convergence in the mean, quadrature convergence does hold for all four Chebyshev w...
متن کاملPointwise convergence of derivatives of Lagrange interpolation polynomials for exponential weights
For a general class of exponential weights on the line and on (−1, 1), we study pointwise convergence of the derivatives of Lagrange interpolation. Our weights include even weights of smooth polynomial decay near ±∞ (Freud weights), even weights of faster than smooth polynomial decay near ±∞ (Erdős weights) and even weights which vanish strongly near ±1, for example Pollaczek type weights. 1991...
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ژورنال
عنوان ژورنال: Journal of Computational and Applied Mathematics
سال: 1991
ISSN: 0377-0427
DOI: 10.1016/0377-0427(91)90096-3