A half-wave rectifier will just only give one peak per cycle and for this reason and other reasons is only employed in extremely small power supplies. A full wave rectifier acquires two peaks each cycle and this is the best which can be done with single-phase input. For three-phase inputs a three-phase bridge will provide six peaks per cycle and even higher numbers of peaks can be acquired by using transformer networks placed before the rectifier to transform to a higher phase order.
To further reduce this ripple, a capacitor-input filter can be employed. This complements the reservoir capacitor along with a choke (inductor) and a second filter capacitor that is why a steadier DC output can be acquired across the terminals of the filter capacitor. The choke represents high impedance to the ripple current.
A more general alternative to a filter, and necessary if the DC load is extremely demanding of a smooth supply voltage, is to follow the reservoir capacitor along with a voltage regulator. The reservoir capacitor requires to be large enough to avoid the troughs of the ripple getting below the voltage the DC (direct current) is being regulated to. The regulator serves both to remove/eliminate the last of the ripple and to deal with differences in supply and load characteristics. It would be probable to make use of a smaller reservoir capacitor (these can be large on high-current power supplies) and after that apply some filtering as well as the regulator, but this is not a general strategy. The extreme of this type of approach is to dispense with the reservoir capacitor altogether and put the rectified waveform straight into a choke-input filter. The benefit of this circuit is that the current waveform is smoother and as a result the rectifier no longer has to deal with the current as a large current pulse, but in place of the current delivery is spread over the whole cycle. The downside is that the voltage output is very much lower - almost the average of an AC half-cycle rather than the peak.