The Greek used by Luke is not that clear. It could be that it was the faith of Peter and John which resulted in his healing (see Matthew 10:1; Matthew 17:14–20). They trusted Jesus to give them the power to heal. Alternatively it was the faith of the beggar (see Luke 5:17–26). Perhaps it is safest to assume that both the beggar and the apostles had faith.1 Whatever the case may be, both faith and the subsequent healing come from Jesus. He is the author of faith (Hebrews 12:2) and he is the one who has all authority (Matthew 28:18)
16 And his name by faith in his name has made this man strong whom you see and know, and the faith that is through Jesus has given the man this perfect health in the presence of you all.