numerical%20approximations

SearchAdvancedHelp

(0.001 seconds)

21—24 of 24 matching pages

21: 6.16 Mathematical Applications

… ►Hence if $x=\pi /(2n)$ and $n\to \mathrm{\infty }$, then the limiting value of $S_n(x)$ overshoots $\frac{1}{4}\pi$ by approximately 18%. Similarly if $x=\pi /n$, then the limiting value of $S_n(x)$ undershoots $\frac{1}{4}\pi$ by approximately 10%, and so on. … ►

►►

Figure 6.16.2: The logarithmic integral $\mathrm{li}\left(x\right)$, together with vertical bars indicating the value of $\pi (x)$ for $x=10,20,\mathrm{\dots },1000$. Magnify

22: Bibliography W

… ►

Algorithm 794: Numerical Hankel transform by the Fortran program HANKEL. ACM Trans. Math. Software 25 (2), pp. 240–250.

ⓘ

Notes:

Double-precision Fortran, maximum accuracy 10S.

External Links:

ISSN 0098-3500, Document, GAMS (module 794; package TOMS), ZentralBlatt

Referenced by:

7th item, 10th item.

Encodings:

BibTeX

… ►

A rational approximant for the digamma function. Numer. Algorithms 33 (1-4), pp. 499–507.

ⓘ

Notes:

International Conference on Numerical Algorithms, Vol. I (Marrakesh, 2001)

External Links:

ISSN 1017-1398, Document, MathReview, ZentralBlatt

Referenced by:

§3.9(vi), §5.23(i).

Encodings:

BibTeX

►

Asymptotic Approximations to Truncation Errors of Series Representations for Special Functions. In Algorithms for Approximation, A. Iske and J. Levesley (Eds.), pp. 331–348.

ⓘ

External Links:

ISBN 3-540-33283-9, Document, MathReview Entry, ZentralBlatt

Referenced by:

§2.10(i).

Encodings:

BibTeX

►

Rational Chebyshev approximation. Numer. Math. 10 (4), pp. 289–306.

ⓘ

External Links:

ISSN 0029-599X, Document, MathReview Entry, ZentralBlatt

Referenced by:

§3.11(iii).

Encodings:

BibTeX

… ►

Error bounds for asymptotic approximations of special functions. Ann. Numer. Math. 2 (1-4), pp. 181–197.

ⓘ

Notes:

Special functions (Torino, 1993)

External Links:

ISSN 1021-2655, MathReview (Andrei Martínez Finkelshtein), ZentralBlatt

Referenced by:

§10.21(vi).

Encodings:

BibTeX

…

23: Bibliography O

… ►

On the asymptotic and numerical solution of linear ordinary differential equations. SIAM Rev. 40 (3), pp. 463–495.

ⓘ

External Links:

ISSN 1095-7200, Document, MathReview (W. Balser), ZentralBlatt

Referenced by:

§16.25, §2.7(ii), §3.7(iii).

Encodings:

BibTeX

… ►

Error bounds for stationary phase approximations. SIAM J. Math. Anal. 5 (1), pp. 19–29.

ⓘ

Notes:

See also Olver (1997b)

External Links:

Document, MathReview (L. Berg), ZentralBlatt

Referenced by:

§2.3(iv).

Encodings:

BibTeX

… ►

Asymptotic approximations and error bounds. SIAM Rev. 22 (2), pp. 188–203.

ⓘ

External Links:

ISSN 0036-1445, Document, MathReview (L. Berg), ZentralBlatt

Referenced by:

§2.7(iii).

Encodings:

BibTeX

… ►

The Generalized Exponential Integral. In Approximation and Computation (West Lafayette, IN, 1993), R. V. M. Zahar (Ed.), International Series of Numerical Mathematics, Vol. 119, pp. 497–510.

ⓘ

External Links:

MathReview (Richard B. Paris), ZentralBlatt

Referenced by:

§2.11(iii), §8.19(viii).

Encodings:

BibTeX

… ►

Numerical solution of Riemann-Hilbert problems: Painlevé II. Found. Comput. Math. 11 (2), pp. 153–179.

ⓘ

External Links:

ISSN 1615-3375, Document, FullText, MathReview Entry, ZentralBlatt

Referenced by:

§32.17, §32.17.

Encodings:

BibTeX

…

24: Bibliography G

… ►

Questions of Numerical Condition Related to Polynomials. In Studies in Numerical Analysis, G. H. Golub (Ed.), pp. 140–177.

ⓘ

External Links:

MathReview Entry, ZentralBlatt

Referenced by:

§3.8(vi).

Encodings:

BibTeX

… ►

Numerical Analysis. An Introduction. Birkhäuser Boston Inc., Boston, MA.

ⓘ

External Links:

ISBN 0-8176-3895-4, MathReview (Ian Gladwell), ZentralBlatt

Referenced by:

§3.11(v), §3.11(v), §3.8(iii), §3.8(ii), §3.8(vii), Ch.3.

Encodings:

BibTeX

… ►

Orthogonal Polynomials: Computation and Approximation. Numerical Mathematics and Scientific Computation, Oxford University Press, New York.

ⓘ

Notes:

OPQ, a package of Matlab routines for generating classical and Sobolev orthogonal polynomials, accompanies this book.

External Links:

OPQ, ISBN 0-19-850672-4, MathReview Entry, ZentralBlatt

Referenced by:

(18.2.27), (18.2.28), (18.2.29), (18.2.30), §18.2(ix), §18.40(ii), §18.40(ii), §18.40(i), 3rd item, §3.5(v), Erratum (V1.0.28) for Table 18.3.1.

Encodings:

BibTeX

… ►

Computing complex Airy functions by numerical quadrature. Numer. Algorithms 30 (1), pp. 11–23.

ⓘ

External Links:

ISSN 1017-1398, Document, MathReview (Richard B. Paris), ZentralBlatt

Referenced by:

§9.17(iii).

Encodings:

BibTeX

… ►

Algorithm 939: computation of the Marcum Q-function. ACM Trans. Math. Softw. 40 (3), pp. 20:1–20:21.

ⓘ

Notes:

Includes Fortran program claiming 12S accuracy

External Links:

ISSN 0098-3500, Link, Document, MathReview Entry, ZentralBlatt

Referenced by:

3rd item, §10.77(ix).

Encodings:

BibTeX

…