FastVelo, a fast and efficient pattern recognition package for the Velo

This note describes the new implementation of the Velo pattern recognition package developed in autumn 2010 to cope with the changed requirements for LHCb tracking: No need for RZ track in the trigger, higher collision rate (so called μ) around 2.5 instead of 0.4 and the need for a faster algorithm for HLT1 to cope with the high rate and large occupancy. After describing the main idea, this note describes the algorithm in details with the meaning of the control parameters. Some performance is also given.