quadrature

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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).

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2: 3.5 Quadrature

§3.5 Quadrature

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§3.5(iv) Interpolatory Quadrature Rules

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§3.5(v) Gauss Quadrature

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§3.5(viii) Complex Gauss Quadrature

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3: 5.21 Methods of Computation

… ►Another approach is to apply numerical quadrature (§3.5) to the integral (5.9.2), using paths of steepest descent for the contour. …

4: 35.10 Methods of Computation

… ►Other methods include numerical quadrature applied to double and multiple integral representations. …

5: 8.25 Methods of Computation

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§8.25(ii) Quadrature

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6: 14.32 Methods of Computation

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Quadrature (§3.5) of the integral representations given in §§14.12, 14.19(iii), 14.20(iv), and 14.25; see Segura and Gil (1999) and Gil et al. (2000).

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7: 9.17 Methods of Computation

… ►For details, including the application of a generalized form of Gaussian quadrature, see Gordon (1969, Appendix A) and Schulten et al. (1979). … ►The second method is to apply generalized Gauss–Laguerre quadrature (§3.5(v)) to the integral (9.5.8). … ►For quadrature methods for Scorer functions see Gil et al. (2001), Lee (1980), and Gordon (1970, Appendix A); but see also Gautschi (1983). …

8: 31.8 Solutions via Quadratures

§31.8 Solutions via Quadratures

… ►the Hermite–Darboux method (see Whittaker and Watson (1927, pp. 570–572)) can be applied to construct solutions of (31.2.1) expressed in quadratures, as follows. …

9: 18.38 Mathematical Applications

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Quadrature

►Classical OP’s play a fundamental role in Gaussian quadrature. If the nodes in a quadrature formula with a positive weight function are chosen to be the zeros of the $n$th degree OP with the same weight function, and the interval of orthogonality is the same as the integration range, then the weights in the quadrature formula can be chosen in such a way that the formula is exact for all polynomials of degree not exceeding $2n-1$. … ►

Quadrature “Extended” to Pseudo-Spectral (DVR) Representations of Operators in One and Many Dimensions

►The basic ideas of Gaussian quadrature, and their extensions to non-classical weight functions, and the computation of the corresponding quadrature abscissas and weights, have led to discrete variable representations, or DVRs, of Sturm–Liouville and other differential operators. …

10: Bibliography G

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Stable computation of high order Gauss quadrature rules using discretization for measures in radiation transfer. J. Quant. Spectrosc. Radiat. Transfer 68 (2), pp. 213–223.

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Referenced by:

§18.39(iii).

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Construction of Gauss-Christoffel quadrature formulas. Math. Comp. 22, pp. 251–270.

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External Links:

ISSN 0025-5718, Document, Link, MathReview (R. E. Barnhill)

Referenced by:

§18.39(iii).

Encodings:

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How and how not to check Gaussian quadrature formulae. BIT 23 (2), pp. 209–216.

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External Links:

ISSN 0006-3835, Document, MathReview (G. A. Evans), ZentralBlatt

Referenced by:

§18.40(ii), §3.5(v), §9.17(iii).

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Computation of Bessel and Airy functions and of related Gaussian quadrature formulae. BIT 42 (1), pp. 110–118.

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External Links:

ISSN 0006-3835, Document, MathReview (Khélifa Trimèche), ZentralBlatt

Referenced by:

§10.74(iii), §9.17(iii).

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Radial quadrature for multi exponential integrands. J. Comput. Chem. 24 (4), pp. 732–740.

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Referenced by:

§18.39(iii).

Encodings:

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