Gauss quadrature

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1: 3.5 Quadrature

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§3.5(v) Gauss Quadrature

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Table 3.5.5: Nodes and weights for the 80-point Gauss–Legendre formula.

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$\pm x_k$	$w_k$
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Table 3.5.9: Nodes and weights for the 20-point Gauss–Laguerre formula.

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$x_k$		$w_k$
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Table 3.5.13: Nodes and weights for the 20-point Gauss–Hermite formula.

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$\pm x_k$		$w_k$
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Table 3.5.17: Nodes and weights for the 20-point Gauss formula for the logarithmic weight function.

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$x_k$		$w_k$
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2: 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).

Encodings:

BibTeX

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Algorithm 726: ORTHPOL — a package of routines for generating orthogonal polynomials and Gauss-type quadrature rules. ACM Trans. Math. Software 20 (1), pp. 21–62.

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Notes:

For remark see same journal 24(1998), p. 355.

External Links:

Document, ISSN 0098-3500, GAMS (module 726; package TOMS), ZentralBlatt

Referenced by:

2nd item, §3.5(v), §3.5(v).

Encodings:

BibTeX

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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:

BibTeX

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Gauss quadrature approximations to hypergeometric and confluent hypergeometric functions. J. Comput. Appl. Math. 139 (1), pp. 173–187.

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External Links:

ISSN 0377-0427, Document, MathReview (Hasan Taşeli), ZentralBlatt

Referenced by:

§13.29(iii), §15.19(iii).

Encodings:

BibTeX

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Calculation of Gauss quadrature rules. Math. Comp. 23 (106), pp. 221–230.

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Notes:

Loose microfiche suppl. A1–A10

External Links:

FullText, MathReview (F. Stenger), ZentralBlatt

Referenced by:

§18.39(iii), §3.5(vi).

Encodings:

BibTeX

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3: 15.19 Methods of Computation

… ►Gauss quadrature approximations are discussed in Gautschi (2002b). …

4: 13.29 Methods of Computation

… ►Gauss quadrature methods are discussed in Gautschi (2002b). …

5: Bibliography T

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Is Gauss quadrature better than Clenshaw-Curtis?. SIAM Rev. 50 (1), pp. 67–87.

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External Links:

ISSN 0036-1445, Document, MathReview (Kai Diethelm), ZentralBlatt

Referenced by:

§3.5(iv).

Encodings:

BibTeX

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6: 3.2 Linear Algebra

… ►Lanczos’ method is related to Gauss quadrature considered in §3.5(v). …

7: 9.17 Methods of Computation

… ►The second method is to apply generalized Gauss–Laguerre quadrature (§3.5(v)) to the integral (9.5.8). …

8: 10.74 Methods of Computation

… ►For applications of generalized Gauss–Laguerre quadrature (§3.5(v)) to the evaluation of the modified Bessel functions $K_{\nu }\left(z\right)$ for and see Gautschi (2002a). …

9: 18.2 General Orthogonal Polynomials

… ►For usage of the zeros of an OP in Gauss quadrature see §3.5(v). …

10: 18.3 Definitions

… ►Formula (18.3.1) can be understood as a Gauss-Chebyshev quadrature, see (3.5.22), (3.5.23). …