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

Probabilistic estimation of the rank 1 cross approximation accuracy