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11: 3.6 Linear Difference Equations
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►This is of little consequence if the wanted solution is growing in magnitude at least as fast as any other solution of (3.6.3), and the recursion process is stable.
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►If, as , the wanted solution grows (decays) in magnitude at least as fast as any solution of the corresponding homogeneous equation, then forward (backward) recursion is stable.
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12: 3.7 Ordinary Differential Equations
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►If the solution that we are seeking grows in magnitude at least as fast as all other solutions of (3.7.1) as we pass along from to , then and may be computed in a stable manner for by successive application of (3.7.5) for , beginning with initial values and .
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►Similarly, if is decaying at least as fast as all other solutions along , then we may reverse the labeling of the along and begin with initial values and .
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13: Bibliography P
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Fast analytic formulas for the modified Bessel functions of imaginary order for spectral line broadening calculations.
J. Quantit. Spec. and Rad. Trans. 62 (4), pp. 389–395.
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14: Bibliography B
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Fast evaluation of the gamma function for small rational fractions using complete elliptic integrals of the first kind.
IMA J. Numer. Anal. 12 (4), pp. 519–526.
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Fast multiple-precision evaluation of elementary functions.
J. Assoc. Comput. Mach. 23 (2), pp. 242–251.
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Discrete Cosine and Sine Transforms. General Properties, Fast Algorithms and Integer Approximations.
Elsevier/Academic Press, Amsterdam.
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15: Bibliography F
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Fast computation of incomplete elliptic integral of first kind by half argument transformation.
Numer. Math. 116 (4), pp. 687–719.
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16: Bibliography W
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Fast construction of the Fejér and Clenshaw-Curtis quadrature rules.
BIT 46 (1), pp. 195–202.
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17: 19.27 Asymptotic Approximations and Expansions
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►These series converge but not fast enough, given the complicated nature of their terms, to be very useful in practice.
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18: Bibliography
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Algorithm 588. Fast Hankel transforms using related and lagged convolutions.
ACM Trans. Math. Software 8 (4), pp. 369–370.
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19: Bibliography D
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A fast new public code for computing photon orbits in a Kerr spacetime.
The Astrophysical Journal 696, pp. 1616–1629.
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20: Bibliography G
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Fast and accurate computation of the Weber parabolic cylinder function
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IMA J. Numer. Anal. 31 (3), pp. 1194–1216.
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