I copy'n'paste the review by M. Znojil of the paper, Kachmar, V. S., Rusyn, B. P., Shmoĭlov, V. I., Algorithms for computing the values of continued fractions, Zh. Vychisl. Mat. Mat. Fiz. 38 (1998), no. 9, 1436--1451; translation in Comput. Math. Math. Phys. 38 (1998), no. 9, 1375–1390, MR1669146 (99m:65026): 

In a pedagogically oriented communication the authors emphasize that divergent continued fractions may be analysed in a way resembling techniques of re-summation of divergent series. Having this type of application in mind, they review existing algorithms (with a few historical comments added), compare some of their properties (number of operations needed, etc.) and illustrate their characteristic features (precision, stability and the rate of convergence) on a few tabulated numerical examples.