Geodesic
Estimate of the Norm of the Lagrange Interpolation Operator in a Multidimensional Sobolev Space
Matematičeskie zametki, Tome 81 (2007) no. 3, pp. 427-433.

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We obtain an estimate of the norm of the Lagrange interpolation operator in a multidimensional Sobolev space. It is shown that, under a suitable choice of the sequence of multi-indices, interpolation polynomials converge to the interpolated function and their rate of convergence is of the order of the best approximation of this function.
Keywords: Lagrange interpolation operator, rate of convergence, best approximation, Sobolev space, Hilbert space.
Mots-clés : interpolation polynomial 
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     author = {A. I. Fedotov},
     title = {Estimate of the {Norm} of the {Lagrange} {Interpolation} {Operator} in a {Multidimensional} {Sobolev} {Space}},
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A. I. Fedotov. Estimate of the Norm of the Lagrange Interpolation Operator in a Multidimensional Sobolev Space. Matematičeskie zametki, Tome 81 (2007) no. 3, pp. 427-433. http://geodesic.mathdoc.fr/item/MZM_2007_81_3_a10/

[1] A. I. Fedotov, “On the asymptotic convergence of the polynomial collocation method for singular integral equations and periodic pseudodifferential equations”, Arch. Math. (Brno), 38:1 (2002), 1–13 | MR | Zbl

[2] M. Teilor, Psevdodifferentsialnye operatory, Mir, M., 1985 | MR | Zbl