quadrature

SearchAdvancedHelp

(0.000 seconds)

21—30 of 36 matching pages

21: Bibliography R

… ►

Universality properties of Gaussian quadrature, the derivative rule, and a novel approach to Stieltjes inversion.

ⓘ

Notes:

arXiv:1812.02196

Referenced by:

§18.40(ii).

Encodings:

BibTeX

… ►

Computation of electron repulsion integrals using the Rys quadrature method. J. Comput. Chem. 4 (2), pp. 154–175.

ⓘ

External Links:

Link

Referenced by:

§18.32, §18.39(iii).

Encodings:

BibTeX

22: Bibliography E

… ►

The numerical inversion of two classes of Kontorovich-Lebedev transform by direct quadrature. J. Comput. Appl. Math. 61 (1), pp. 43–72.

ⓘ

External Links:

ISSN 0377-0427, Document, MathReview (J. P. Singhal), ZentralBlatt

Referenced by:

§10.74(vii).

Encodings:

BibTeX

…

23: 18.39 Applications in the Physical Sciences

… ►For many applications the natural weight functions are non-classical, and thus the OP’s and the determination of the Gaussian quadrature points and weights represent a computational challenge. … ►

Table 18.39.1: Typical Non-Classical Weight Functions Of Use In DVR Applications^a

► ►►►

Name of OP System	$w(x)$	$[a,b]$	Notation	Applications
…
Multi-Exponential	${\ln }^{2}x$	$[0,1]$	$MEx{p}_n(x)$	Quadrature Sums of Exponentialsk
…

►

… ►Full expressions for both $A_{x_i,l}$ and $B_l(x)$ are given in Yamani and Reinhardt (1975) and it is seen that ${|A_{x_i,l}/B_l(x_i)|}^2$ = $w_i^N/w^{\mathrm{CP}}(x_i)$ where $w_i^N$ is the Gaussian-Pollaczek quadrature weight at $x=x_i$, and $w^{\mathrm{CP}}(x_i)$ is the Gaussian-Pollaczek weight function at the same quadrature abscissa. This equivalent quadrature relationship, see Heller et al. (1973), Yamani and Reinhardt (1975), allows extraction of scattering information from the finite dimensional $L^2$ functions of (18.39.53), provided that such information involves potentials, or projections onto $L^2$ functions, exactly expressed, or well approximated, in the finite basis of (18.39.44). The equivalent quadrature weight, $w_i/w^{\mathrm{CP}}(x_i)$, also forms the foundation of a novel inversion of the Stieltjes–Perron moment inversion discussed in §18.40(ii). …

24: 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). …

25: 13.29 Methods of Computation

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

26: 3.2 Linear Algebra

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

27: Bibliography B

… ►

Numerical evaluation of the zero-order Hankel transform using Filon quadrature philosophy. Appl. Math. Lett. 9 (5), pp. 21–26.

ⓘ

External Links:

ISSN 0893-9659, Document, MathReview, ZentralBlatt

Referenced by:

§10.74(vii).

Encodings:

BibTeX

… ►

New Aspects in Numerical Quadrature. In Proc. Sympos. Appl. Math., Vol. XV, pp. 199–218.

ⓘ

External Links:

MathReview (S. Haber), ZentralBlatt

Referenced by:

§3.5(iii).

Encodings:

BibTeX

… ►

Interpolation und genäherte Quadratur. In Mathematische Hilfsmittel des Ingenieurs. Teil III, R. Sauer and I. Szabó (Eds.), Die Grundlehren der mathematischen Wissenschaften in Einzeldarstellungen, Vol. 141, pp. 232–319.

ⓘ

External Links:

MathReview (E. Kreyszig)

Referenced by:

§3.3(vi).

Encodings:

BibTeX

…

28: Bibliography H

… ►

On an “equivalent quadrature” calculation of matrix elements of ${(z-p^2/2m)}^{-1}$ using an $L^2$ expansion technique. J. Comput. Phys. 13, pp. 536–550.

ⓘ

External Links:

Document, Link

Referenced by:

§18.39(iv).

Encodings:

BibTeX

…

29: 18.36 Miscellaneous Polynomials

… ►EOP’s are non-classical in that not only are certain polynomial orders missing, but, also, not all EOP polynomial zeros are within the integration range of their generating measure, and EOP-orthogonality properties do not allow development of Gaussian-type quadratures. …

30: Bibliography C

… ►

A quadrature formula for the Hankel transform. Numer. Algorithms 9 (2), pp. 343–354.

ⓘ

External Links:

ISSN 1017-1398, Document, MathReview (V. I. Polovinkin), ZentralBlatt

Referenced by:

§10.74(vii).

Encodings:

BibTeX

… ►

Numerical integration of related Hankel transforms by quadrature and continued fraction expansion. Geophysics 48 (12), pp. 1671–1686.

ⓘ

Notes:

Fortran code.

External Links:

ISSN 0098-3500, Document

Referenced by:

§10.77(ix).

Encodings:

BibTeX

…