On Lagrange interpolation with equally spaced nodes
نویسندگان
چکیده
منابع مشابه
On Lagrange Interpolation with Equidistant Nodes
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 , . . . ) ...
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We present two results that quantify the poor behavior of polynomial interpolation in n equally spaced points. First, in band-limited interpolation of complex exponential functions e‘li (c( E Iw), the error decreases to 0 as n + a, if and only if d( is small enough to provide at least six points per wavelength. Second, the Lebesgue constant ,4. (supremum norm of the nth interpolation operator) ...
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ژورنال
عنوان ژورنال: Bulletin of the Australian Mathematical Society
سال: 2000
ISSN: 0004-9727,1755-1633
DOI: 10.1017/s0004972700018876