On Lagrange Interpolation with Equidistant Nodes
نویسندگان
چکیده
In 1918 Bernstein [2] published a result concerning the divergence of Lagrange interpolation based on equidistant nodes. This result, which now has a prominent place in the study of the appoximation of functions by interpolation polynomials, may be described as follows. Throughout this paper let / (* ) = |x| (—1 < x < 1) and Xk,n = 1 + 2(fcl ) / ( n l ) (Jfe = 1,2,... ,n; n = 1 ,2 ,3 , . . . ) . Define the Lagrange interpolation polynomial of degree n — 1 to be the unique polynomial Ln^i(f,x) of degree n — 1 or less which satisfies the n conditions
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