Algorithms for the computation of the values of the modified Bessel functions of the first and second kind
for complex values of
are given. The algorithm for the computation of the Bessel function
is based on the so-called Miller-Olver algorithm, and the algorithm for the computation of
on the algorithm by N. M. Temme
[J. Comput. Phys. 19, 324–337 (1975; Zbl 0334.65013
)]. The authors consider also a program realization of the algorithms. The results of numerical experiments are given and discussed.