for Padé approximations

SearchAdvancedHelp

(0.002 seconds)

1—10 of 13 matching pages

1: 4.47 Approximations

… ►

§4.47(iii) Padé Approximations

…

2: 19.38 Approximations

… ►Approximations for Legendre’s complete or incomplete integrals of all three kinds, derived by Padé approximation of the square root in the integrand, are given in Luke (1968, 1970). …

3: 3.11 Approximation Techniques

… ►

§3.11(iv) Padé Approximations

… ► … ► … ►Any five approximants arranged in the Padé table as … ►For further information on Padé approximations, see Baker and Graves-Morris (1996, §4.7), Brezinski (1980, pp. 9–39 and 126–177), and Lorentzen and Waadeland (1992, pp. 367–395). …

4: 8.27 Approximations

… ►

Luke (1975, §4.3) gives Padé approximation methods, combined with a detailed analysis of the error terms, valid for real and complex variables except on the negative real $z$-axis. See also Temme (1994b, §3).

… ►

Luke (1975, p. 106) gives rational and Padé approximations, with remainders, for $E_1\left(z\right)$ and $z^{-1}{\int }_0^z{t}^{-1}(1-{\mathrm{e}}^{-t})dt$ for complex $z$ with $\left|\mathrm{ph}z\right|\le \pi$.

…

5: 13.31 Approximations

… ►

§13.31(ii) Padé Approximations

…

6: 7.24 Approximations

… ►

Luke (1969b, vol. 2, pp. 422–435) gives main diagonal Padé approximations for $F\left(z\right)$, $\mathrm{erf}z$, $\mathrm{erfc}z$, $C\left(z\right)$, and $S\left(z\right)$; approximate errors are given for a selection of $z$-values.

7: 6.20 Approximations

… ►

Luke (1969b, pp. 402, 410, and 415–421) gives main diagonal Padé approximations for $\mathrm{Ein}\left(z\right)$, $\mathrm{Si}\left(z\right)$, $\mathrm{Cin}\left(z\right)$ (valid near the origin), and $E_1\left(z\right)$ (valid for large $|z|$); approximate errors are given for a selection of $z$-values.

…

8: 18.36 Miscellaneous Polynomials

… ►They are related to Hermite–Padé approximation and can be used for proofs of irrationality or transcendence of interesting numbers. …

9: Bibliography B

… ►

Padé-type Approximation and General Orthogonal Polynomials. International Series of Numerical Mathematics, Vol. 50, Birkhäuser Verlag, Basel.

ⓘ

External Links:

ISBN 3-7643-1100-2, MathReview (A. Magnus), ZentralBlatt

Referenced by:

§3.11(iv).

Encodings:

BibTeX

…

10: 18.40 Methods of Computation

… ►The question is then: how is this possible given only $F_N(z)$, rather than $F(z)$ itself? $F_N(z)$ often converges to smooth results for $z$ off the real axis for $\mathrm{\Im }z$ at a distance greater than the pole spacing of the $x_n$, this may then be followed by approximate numerical analytic continuation via fitting to lower order continued fractions (either Padé, see §3.11(iv), or pointwise continued fraction approximants, see Schlessinger (1968, Appendix)), to $F_N(z)$ and evaluating these on the real axis in regions of higher pole density that those of the approximating function. …