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A Stable Quotient-Difference Algorithm
A. N. Stokes
Mathematics of Computation
Vol. 34, No. 150 (Apr., 1980), pp. 515-519
Published by: American Mathematical Society
Stable URL: http://www.jstor.org/stable/2006099
Page Count: 5
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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.
Mathematics of Computation © 1980 American Mathematical Society