Partial water changes do not speed up the cycle. In actuality it slows down the process. By taking away ammonia, the food source for nitrosomonas or nitrifying bacteria, you reduce the number of bacteria which then inhibits the amount of nitrobacters, or the bacteria which feeds on nitrites and produces nitrate as a result. PWC
are only done during a fish in cycle in order to help keep the fish alive by keeping toxins down. To have a healthy fast cycle you must let nature take it's course and not deplete ammonia or nitrite until cycle is complete.