  We study renormalization in a scalar field theory on the fuzzy sphere. The
theory is realized by a matrix model, where the matrix size plays the role of a
UV cutoff. We define correlation functions by using the Berezin symbol
identified with a field and calculate them nonperturbatively by Monte Carlo
simulation. We find that the 2-point and 4-point functions are made independent
of the matrix size by tuning a parameter and performing a wave function
renormalization. The results strongly suggest that the theory is
nonperturbatively renormalizable in the ordinary sense.
