Algorithms A and B provide good performance.
Algorithms A and B provide good performances.
Could you please tell me which one between the above sentences is correct ?
Algorithm A provides good performance.
Algorithm A provides a good performance.
Also, between the above sentences, which one is correct ? In other words, is performance countable or uncountable in this context?
Performance is uncountable in this context. So you want:
Algorithms A and B provide good performance.
and
Algorithm A provides good performance.
I do think this is the sort of thing where you might find some disagreement. Abstract nouns like "performance" and "speed" can be interpreted as quantifiable properties, or scores, in which case they would be countable.
The speeds of the two cars were 45 kph and 80 kph, respectively.
But you could also say of two football players (whatever the flavor of football)
Smith and Jones have excellent speed.
"Performance," in the sense of algorithm speed, is a fairly new term. It still sounds awkward to me to say "This table gives the performances of the different algorithms," even though it fits the pattern of the "speed" examples. But you will definitely find that phrasing in the scientific literature.
In the examples you gave, however, the non-countable forms are definitely preferred.
