In this paper we study the quantities [formula] which define error bounds for the
approximation of functions ƒ∈ Wm∞[a, b] by the interpolating Lagrange polynomials lm− 1 …

In 1918 SN Bernstein published the surprising result that the sequence of Lagrange
interpolation polynomials to| x| at equally spaced nodes in [− 1, 1] diverges everywhere …

For f:[-1,+ 1]––> R let pn (x)= L n (f; x) be the Lagrange interpolation polynomial on the roots
of the Chebyshev polynomial of degree n: pn (\cos\theta m, n)= f (\cos\theta m, n), m= 1,..., n …

It is a classical result of Bernstein that the sequence of Lagrange interpolation polynomials
to| x| at equally spaced nodes in [− 1, 1] diverges everywhere, except at zero and the end …

On the asymptotics of polynomial interpolation to |x|α at the Chebyshev nodes -
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In this paper we prove three conjectures of Revers on Lagrange interpolation for fλ (t)=| t| λ,
λ> 0, at equidistant nodes. In particular, we describe the rate of divergence of the Lagrange …

It is shown that for any n+ 1 times continuously differentiable function f and any choice of n+
1 knots, the Lagrange interpolation polynomial L of degree n satisfies∥ f (n)− L (n)∥⩽∥ ω …

Further, let 1> xln (w)> xZn (w)>.**> x,,(w)>-1 be the zeros of pn (w, x). For a continuous
functionf on [-1, 11, the Lagrange interpolation polynomial L,(w, f) is defined to be the unique …

The Lebesgue constant for Lagrange interpolation on equidistant nodes Page 1 Numer. Math.
61, 111-115 (1992) Numerische MathemaUk 9 Springer-Verlag 1992 The Lebesgue constant …

We construct the polynomial pm, n∗ of degree m which interpolates a given real-valued
function f∈ L2 [a, b] at pre-assigned n distinct nodes and is the best approximant to f in the …