Numerical computation of continued fractions

If K(an/bn) converges generally to f, then its approximants {Sn(wn)} converge to f as long as {wn} stays asymptotically away from its exceptional sequence. Therefore we can use Sn(wn) as an approximation to f. However, the choice of {w makes quite a difference. For one thing, if one is looking for, say, a rational approximant, then this limits the choice for {wn. But often one just wants fast convergence to f. In this chapter we suggest a number of ideas for how to choose wn to this aim.