iterative refinement

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11: 18.20 Hahn Class: Explicit Representations

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12: Bibliography J

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Memoire sur l’itération des fonctions rationnelles. J. Math. Pures Appl. 8 (1), pp. 47–245 (French).

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External Links:

FullText, ZentralBlatt

Referenced by:

§3.8(viii).

Encodings:

BibTeX

13: Bibliography O

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Iterative Solution of Nonlinear Equations in Several Variables. Academic Press, New York.

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Notes:

Reprinted in 2000 by the Society for Industrial and Applied Mathematics (SIAM), Philadelphia, Pennsylvania

External Links:

MathReview (J. F. Traub), ZentralBlatt (Nelli Dimitrova (Sofia))

Referenced by:

§3.8(vii).

Encodings:

BibTeX

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14: Bibliography T

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Iterative Methods for the Solution of Equations. Prentice-Hall Series in Automatic Computation, Prentice-Hall Inc., Englewood Cliffs, N.J..

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External Links:

MathReview (W. C. Rheinboldt), ZentralBlatt

Referenced by:

§3.8(iii).

Encodings:

BibTeX

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15: Bibliography S

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Time propagation of partial differential equations using the short iterative Lanczos method and finite-element discrete variable representation. Adv. Quantum Chem. 72, pp. 95–127.

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Referenced by:

§18.38(i).

Encodings:

BibTeX

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The accuracy of iterated JWBK approximations for Coulomb radial functions. Comput. Phys. Comm. 32 (2), pp. 115–119.

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External Links:

Document

Referenced by:

§33.23(vii).

Encodings:

BibTeX

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Bounds on differences of adjacent zeros of Bessel functions and iterative relations between consecutive zeros. Math. Comp. 70 (235), pp. 1205–1220.

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External Links:

ISSN 0025-5718, Document, MathReview (Boro Döring), ZentralBlatt

Referenced by:

§10.74(vi).

Encodings:

BibTeX

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16: 19.36 Methods of Computation

… ►When the differences are moderately small, the iteration is stopped, the elementary symmetric functions of certain differences are calculated, and a polynomial consisting of a fixed number of terms of the sum in (19.19.7) is evaluated. … ►If the iteration of (19.36.6) and (19.36.12) is stopped when ($M$ and $T$ being approximated by $a_s$ and $t_s$, and the infinite series being truncated), then the relative error in $R_F$ and $R_G$ is less than $r$ if we neglect terms of order $r^2$. …

17: 2.10 Sums and Sequences

… ►This result is refinable in two important ways. …

18: 3.5 Quadrature

… ►Simpson’s rule can be regarded as a combination of two trapezoidal rules, one with step size $h$ and one with step size $h/2$ to refine the error term. … ►Further refinements are achieved by Romberg integration. …

19: 3.10 Continued Fractions

… ►To compute the $C_n$ of (3.10.2) we perform the iterated divisions …

20: 19.5 Maclaurin and Related Expansions

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