How to Increase Alternate Picking Speed
If the down-up alternation itself (see [[alternate-picking-basics:the article on alternate picking]]) is already solid, the next question isn't technique - it's the method of training speed, and 'just play faster' isn't it.
The +5 BPM method: only after three clean passes
Raise the metronome in small steps (5 BPM), and only once the current tempo has been played cleanly three times in a row with zero mistakes. Raising tempo 'on a schedule' instead of 'on readiness' is the most common reason speed grows slower than it could.
The 'speed burst' trick for breaking through a ceiling
If a tempo has been stuck for weeks, play just 2-4 notes at a tempo noticeably above your target (say, 20-30 BPM higher), then stop immediately. This trains the muscles' raw speed capacity separately from endurance - after a few days of these bursts, the usual 'working' tempo often feels easier.
Find your single slowest transition
Every passage has one specific string or note change that caps the speed of the whole thing (the same principle as in the article on string crossing, see the article on crossing strings) - drill exactly that one on its own, not the whole passage with equal attention.
Tension builds up unnoticed - check the hand
At high tempo, tension in the wrist and forearm builds up without the player noticing - stop periodically and deliberately check whether the hand has tensed up (see the article on speed and cleanliness). A tense hand is physically slower than a relaxed one, so training right at the edge of tension is often the real ceiling, not the mechanics itself.
Drill on a short scale
Take one pentatonic position (see the article on getting started improvising) and apply the +5 BPM method right there - short, familiar material lets you focus on the mechanics of speed itself, not on which notes come next.
Try it in practice
Open the metronome