When picking multiple notes on a string, alternate picking (alternating between downstrokes and upstrokes) is used.
When changing to a new string, sweep picking (picking in the direction of travel: downstroke if moving down or upstroke when moving up) is used.
This minimises movement in the picking hand, and avoids the motion of "jumping" over a string prior to picking it, as often occurs in alternate-picking when changing strings. Thus the picking pattern of an ascending three-note-per-string scale would be: D-U-D-D-U-D-D-U-D, and the descending pattern would start just like alternate picking (up stroke first): U-D-U-U-D-U-U-D-U.
Using two or more downstrokes or upstrokes in a row to execute lines had been a technique used in jazz since at least, the 1950s, but it is Frank Gambale who is probably the most widely known economy or sweep picker. Frank brought his technique to America from Australia in 1982 and had a huge influence on the Heavy Metal community, first as a student (graduating with high honors), and then as a teacher at the Guitar Institute of Technology, which is part of the Musicians Institute of Technology in Hollywood, California. Frank was the first player to fully develop this technique and apply it to all scales and arpeggios. Frank uses a system of an odd number of notes to move up or down through the strings and an even amount of notes to change direction. He makes this observation in his instructional books and videos. This approach has taken some criticism as Frank will skip a note in a scale, or add a chromatic note to ensure an even amount of notes to facilitate changing direction. Therefore, the scale is no longer purely ascended and descended. An alternative approach that maintains the purity of the scale, and satisfies the even number of notes rule to change direction, is to ascend one 3 note per string shape and then descend the next. This way there are 4 notes played in total on the high E string and the low E string. These two shapes can be cycled making a repetitive exercise for economy picking.
Guitarists known for their economy picking technique
Yngwie Malmsteen can be heard using sweep picking in his 1978 Demo "Powerhouse". Yngwie sent his demo to Mark Varney of Shrapnel Records, and Mark invited Yngwie to come out to California. Yngwie made the trip from Sweden in late 1982 and joined the band Steeler, who were under the Shrapnel Records label. Yngwie was playing live in the LA scene with Steeler in 1983.
Gambale and Malmsteen share credit for introducing sweep picking to LA guitar players and ultimately, to the rest of the world.
Les Paul can be see performing economy/sweep picking in this 1953 video at 1:10
Eric Johnson uses this technique in songs like "Cliffs of Dover"
Jan Akkerman the guitarist of the Dutch band Focus can be seen executing a swept arpeggio on the NBC show "Midnight Special" October 5, 1973 during a performance of the Focus song "Hocus Pocus" at 2:53
Chet Atkins can also been seen performing 5 string sweeps in an 1975 performance of "Jerry's Breakdown" with fellow country picker Jerry Reed at 1:13
Yngwie Malmsteen makes extensive use of sweep picking in his 1984 release "Rising Force" as does Vinnie Moore in his 1986 release "Mind's Eye"
The picking technique of gypsy jazz has been described as similar to economy picking, but with the further requirement that when pattern switches from string to string in either direction, a rest stroke will be performed. For instance, on switching from the G to the B string, the plectrum will move in the same direction and come to rest on the E string. However, on switching from the B to the G string, the plectrum will move upward and execute a down stroke on the G string, again coming to rest on the B string. This technique was employed by gypsy guitarist Django Reinhardt and has been preserved by gypsy guitarists. However, he did not invent it. Exactly why Django used that technique is a bit of a mystery. He may have learned it from other gypsy players, of whom two of his chief influences were banjoist Gusti Mahla and guitarist Jean "Poulette" Castro. However, the technique was commonly taught in numerous guitar methods in the early twentieth century and also employed by American jazz banjo players.