Lagrange interpolation

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1: 3.3 Interpolation
§3.3(i) LagrangeInterpolation
With an error term the Lagrange interpolation formula for $f$ is given by …
2: 18.40 Methods of Computation
In what follows this is accomplished in two ways: i) via the Lagrange interpolation of §3.3(i) ; and ii) by constructing a pointwise continued fraction, or PWCF, as follows: … Comparisons of the precisions of Lagrange and PWCF interpolations to obtain the derivatives, are shown in Figure 18.40.2. …
3: Bibliography G
• W. Gautschi (1992) On mean convergence of extended Lagrange interpolation. J. Comput. Appl. Math. 43 (1-2), pp. 19–35.
• 4: 3.11 Approximation Techniques
If $J=n+1$, then $p_{n}(x)$ is the Lagrange interpolation polynomial for the set $x_{1},x_{2},\dots,x_{J}$3.3(i)). … For many applications a spline function is a more adaptable approximating tool than the Lagrange interpolation polynomial involving a comparable number of parameters; see §3.3(i), where a single polynomial is used for interpolating $f(x)$ on the complete interval $[a,b]$. …
5: Bibliography B
• J. Berrut and L. N. Trefethen (2004) Barycentric Lagrange interpolation. SIAM Rev. 46 (3), pp. 501–517.
The nodes $x_{1},x_{2},\dots,x_{n}$ are prescribed, and the weights $w_{k}$ and error term $E_{n}(f)$ are found by integrating the product of the Lagrange interpolation polynomial of degree $n-1$ and $w(x)$. …
The Lagrange $(n+1)$-point formula is …The $B_{k}^{n}$ are the differentiated Lagrangian interpolation coefficients:
3.4.2 $B_{k}^{n}=\ifrac{\mathrm{d}A_{k}^{n}}{\mathrm{d}t},$