  In the construction of low-rank matrix approximation and maximum element
search it is effective to use maxvol algorithm. Nevertheless, even in the case
of rank 1 approximation the algorithm does not always converge to the maximum
matrix element, and it is unclear how often close to the maximum element can be
found. In this article it is shown that with a certain degree of randomness in
the matrix and proper selection of the starting column, the algorithm with high
probability in a few steps converges to an element, which module differs little
from the maximum. It is also shown that with more severe restrictions on the
error matrix no restrictions on the starting column need to be introduced.
