# interpolation

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## 1—10 of 19 matching pages

##### 1: Bibliography X

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Prolate spheroidal wavefunctions, quadrature and interpolation.
Inverse Problems 17 (4), pp. 805–838.
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##### 2: 3.3 Interpolation

###### §3.3 Interpolation

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

… ►###### Linear Interpolation

… ►###### §3.3(v) Inverse Interpolation

… ►###### §3.3(vi) Other Interpolation Methods

…##### 3: Annie A. M. Cuyt

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►A lot of her research has been devoted to rational approximations, in one as well as in many variables, and sparse interpolation.
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##### 4: 18.40 Methods of Computation

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►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 $N=120$.
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►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.
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##### 5: 3.4 Differentiation

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►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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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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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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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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##### 6: Philip J. Davis

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