Newton interpolation formula

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1: 3.3 Interpolation

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§3.3(iv) Newton’s Interpolation Formula

… ►For comparison, we use Newton’s interpolation formula (3.3.38) …Then by using $x_3$ in Newton’s interpolation formula, evaluating $\left[x_0,x_1,x_2,x_3\right]f=-\mathrm{0.26608\hspace{0.33em}28233}$ and recomputing $f^{\prime }(x)$, another application of Newton’s rule with starting value $x_3$ gives the approximation $x=\mathrm{2.33810\hspace{0.33em}7373}$, with 8 correct digits. …

2: 3.5 Quadrature

… ► ►Rules of closed type include the Newton–Cotes formulas such as the trapezoidal rules and Simpson’s rule. … ► … ►

Gauss–Laguerre Formula

… ►a complex Gauss quadrature formula is available. …

3: 3.8 Nonlinear Equations

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§3.8(ii) Newton’s Rule

… ► … ►Newton’s rule is given by … ►

Regula Falsi

… ►Newton’s method is given by …