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Mathematics of Computation

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A stable quotient-difference algorithm

Author: A. N. Stokes
Journal: Math. Comp. 34 (1980), 515-519
MSC: Primary 65D15; Secondary 41A21
MathSciNet review: 559199
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Abstract: This paper shows how the arithmetic of the quotient-difference algorithm can be performed using the forward and backward difference tables of each column. This removes the tendency of the algorithm to amplify errors. As an application, 70 continued fraction coefficients are calculated for the modified Bessel function ${K_0}(z)$ in single-precision arithmetic. There is no significant build-up of error.

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Article copyright: © Copyright 1980 American Mathematical Society