# Lagrange interpolation

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## 7 matching pages

##### 1: 3.3 Interpolation

###### §3.3 Interpolation

►###### §3.3(i) Lagrange Interpolation

… ► ►With an error term the*Lagrange interpolation formula*for $f$ is given by … ►

###### §3.3(ii) Lagrange Interpolation with Equally-Spaced Nodes

…##### 2: 18.40 Methods of Computation

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►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:
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►Comparisons of the precisions of Lagrange and PWCF interpolations to obtain the derivatives, are shown in Figure 18.40.2.
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##### 3: Bibliography G

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On mean convergence of extended Lagrange interpolation.
J. Comput. Appl. Math. 43 (1-2), pp. 19–35.
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##### 4: 3.11 Approximation Techniques

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►If $J=n+1$, then ${p}_{n}(x)$ is the Lagrange interpolation polynomial for the set ${x}_{1},{x}_{2},\mathrm{\dots},{x}_{J}$ (§3.3(i)).
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►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 $[a,b]$.
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##### 5: Bibliography B

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Barycentric Lagrange interpolation.
SIAM Rev. 46 (3), pp. 501–517.
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##### 6: 3.5 Quadrature

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►The

*nodes*${x}_{1},{x}_{2},\mathrm{\dots},{x}_{n}$ 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 $w(x)$. …