Simpson rule

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21: 1.5 Calculus of Two or More Variables

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Chain Rule

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22: 4.45 Methods of Computation

… ►For $x\in [-1/\mathrm{e},\mathrm{\infty })$ the principal branch $\mathrm{Wp}\left(x\right)$ can be computed by solving the defining equation $W{\mathrm{e}}^W=x$ numerically, for example, by Newton’s rule (§3.8(ii)). …

23: 13.29 Methods of Computation

… ►In Allasia and Besenghi (1991) and Allasia and Besenghi (1987a) the high accuracy of the trapezoidal rule for the computation of Kummer functions is described. …

24: 17.2 Calculus

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Product Rule

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Leibniz Rule

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25: Bibliography T

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The numerical computation of special functions by use of quadrature rules for saddle point integrals. II. Gamma functions, modified Bessel functions and parabolic cylinder functions. Report TW 183/78 Mathematisch Centrum, Amsterdam, Afdeling Toegepaste Wiskunde.

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Notes:

Algol procedures, maximum accuracy 14S.

External Links:

FullText, ZentralBlatt

Referenced by:

§12.21(ii).

Encodings:

BibTeX

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26: 3.11 Approximation Techniques

… ►The Padé approximants can be computed by Wynn’s cross rule. Any five approximants arranged in the Padé table as …

27: 3.4 Differentiation

… ►The integral on the right-hand side can be approximated by the composite trapezoidal rule (3.5.2). … ►As explained in §§3.5(i) and 3.5(ix) the composite trapezoidal rule can be very efficient for computing integrals with analytic periodic integrands. …

28: Bibliography W

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Fast construction of the Fejér and Clenshaw-Curtis quadrature rules. BIT 46 (1), pp. 195–202.

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External Links:

ISSN 0006-3835, Document, MathReview Entry, ZentralBlatt

Referenced by:

§3.5(iv).

Encodings:

BibTeX

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29: Software Index

… ►Please see our Software Indexing Policy for rules that govern the indexing of software in the DLMF. …

30: 3.3 Interpolation

… ►and compute an approximation to $a_1$ by using Newton’s rule (§3.8(ii)) with starting value $x=-2.5$. …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. …