interpolation

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1: Bibliography X

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Prolate spheroidal wavefunctions, quadrature and interpolation. Inverse Problems 17 (4), pp. 805–838.

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Notes:

Special issue to celebrate Pierre Sabatier’s 65th birthday (Montpellier, 2000)

External Links:

ISSN 0266-5611, Document, MathReview (Thomas Sauer), ZentralBlatt

Referenced by:

§30.13(v).

Encodings:

BibTeX

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2: 3.3 Interpolation

§3.3 Interpolation

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§3.3(i) Lagrange Interpolation

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Linear Interpolation

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§3.3(v) Inverse Interpolation

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§3.3(vi) Other Interpolation Methods

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3: Annie A. M. Cuyt

… ►A lot of her research has been devoted to rational approximations, in one as well as in many variables, and sparse interpolation. …

4: 18.40 Methods of Computation

… ►Interpolation of the midpoints of the jumps followed by differentiation with respect to $x$ yields a Stieltjes–Perron inversion to obtain $w^{\mathrm{RCP}}(x)$ to a precision of $\sim 4$ decimal digits for $N=120$. … ►Here $x(t,N)$ is an interpolation of the abscissas $x_{i,N},i=1,2,\mathrm{\dots },N$, that is, $x(i,N)=x_{i,N}$, allowing differentiation by $i$. 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: …The PWCF $x(t,N)$ is a minimally oscillatory algebraic interpolation of the abscissas $x_{i,N},i=1,2,\mathrm{\dots },N$. ►Comparisons of the precisions of Lagrange and PWCF interpolations to obtain the derivatives, are shown in Figure 18.40.2. …

5: 3.4 Differentiation

… ►The $B_k^n$ are the differentiated Lagrangian interpolation coefficients: ►

3.4.2 $$B_k^n=d{A}_k^n/dt,$$

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Defines:

$B_k^n$: differentiated Lagrangian interpolation coefficients (locally)

Symbols:

$\frac{df}{dx}$: derivative of $f$ with respect to $x$ and $A_k^n$: Lagrangian interpolation coefficients

Referenced by:

§3.4(i)

Permalink:

http://dlmf.nist.gov/3.4.E2

Encodings:

pMML, png, TeX

See also:

Annotations for §3.4(i), §3.4 and Ch.3

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3.4.7 $$h{f}_t^{\prime }=\sum _{k=-1}^2{B}_k^3{f}_k+h{R}_{3,t}^{\prime },$$ ,

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Symbols:

$B_k^n$: differentiated Lagrangian interpolation coefficients and $R_{n,t}^{\prime }(x)$: remainder

A&S Ref:

25.3.5 (modification of)

Permalink:

http://dlmf.nist.gov/3.4.E7

Encodings:

pMML, png, TeX

See also:

Annotations for §3.4(i), §3.4(i), §3.4 and Ch.3

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3.4.11 $$h{f}_t^{\prime }=\sum _{k=-2}^3{B}_k^5{f}_k+h{R}_{5,t}^{\prime },$$ ,

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Symbols:

$B_k^n$: differentiated Lagrangian interpolation coefficients and $R_{n,t}^{\prime }(x)$: remainder

Permalink:

http://dlmf.nist.gov/3.4.E11

Encodings:

pMML, png, TeX

See also:

Annotations for §3.4(i), §3.4(i), §3.4 and Ch.3

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3.4.15 $$h{f}_t^{\prime }=\sum _{k=-3}^4{B}_k^7{f}_k+h{R}_{7,t}^{\prime },$$ ,

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Symbols:

$B_k^n$: differentiated Lagrangian interpolation coefficients and $R_{n,t}^{\prime }(x)$: remainder

Permalink:

http://dlmf.nist.gov/3.4.E15

Encodings:

pMML, png, TeX

See also:

Annotations for §3.4(i), §3.4(i), §3.4 and Ch.3

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6: Philip J. Davis

… ►Davis also co-authored a second Chapter, “Numerical Interpolation, Differentiation, and Integration” with Ivan Polonsky. …

7: 3.8 Nonlinear Equations

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Regula Falsi

… ►Inverse linear interpolation (§3.3(v)) is used to obtain the first approximation: …

8: Bibliography N

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Tables of Lagrangian Interpolation Coefficients. Columbia University Press, New York.

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Notes:

Technical Director: Arnold N. Lowan

External Links:

MathReview (W. Feller), ZentralBlatt

Referenced by:

§3.3(ii).

Encodings:

BibTeX

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9: Bibliography P

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On the maximum errors of polynomial approximations defined by interpolation and by least squares criteria. Comput. J. 9 (4), pp. 404–407.

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External Links:

Document, MathReview, ZentralBlatt

Referenced by:

§3.11(ii).

Encodings:

BibTeX

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10: Bibliography T

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Six myths of polynomial interpolation and quadrature. Math. Today (Southend-on-Sea) 47 (4), pp. 184–188.

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External Links:

FullText

Referenced by:

§3.5(iv), §3.5(iv), Ch.3.

Encodings:

BibTeX

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