Lagrange interpolation
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1: 3.3 Interpolation
§3.3 Interpolation
►§3.3(i) Lagrange Interpolation
… ► ►With an error term the Lagrange interpolation formula for 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 , then is the Lagrange interpolation polynomial for the set (§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
on the complete interval .
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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
are prescribed, and the weights
and error term
are found by integrating the product of the Lagrange interpolation polynomial of degree and .
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