A stable quotient-difference algorithm
A. N. Stokes · Mathematics of Computation · 1980
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 ) {K_0}(z) in single-precision arithmetic. There is no significant build-up of error.