iterative refinement
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11—20 of 23 matching pages
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).
13: Bibliography O
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Iterative Solution of Nonlinear Equations in Several Variables.
Academic Press, New York.
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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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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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The accuracy of iterated JWBK approximations for Coulomb radial functions.
Comput. Phys. Comm. 32 (2), pp. 115–119.
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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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16: 19.36 Methods of Computation
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►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.
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►If the iteration of (19.36.6) and (19.36.12) is stopped when ( and being approximated by and , and the infinite series being truncated), then the relative error in and is less than if we neglect terms of order .
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17: 2.10 Sums and Sequences
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►This result is refinable in two important ways.
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18: 3.5 Quadrature
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►Simpson’s rule can be regarded as a combination of two trapezoidal rules, one with step size and one with step size to refine the error term.
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►Further refinements are achieved by Romberg integration.
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19: 3.10 Continued Fractions
20: 19.5 Maclaurin and Related Expansions
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